You're very welcome Gifty Asare! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
@@xsageonexx7399 Take, for example; x + b Square it: (x + b)(x + b), and carry out the multiplication to get the product: x^2 + 2bx + b^2 In the example polynomial, the 7/6 coefficient is your 2b, so you need to divide by 2, or multiply by 1/2 to get the value of b to add to the L-value to produce a perfect square.
I'm French. I'm retired (after a professional career in data processing). I love mathematics (it doesn't mean I'm an expert of it :-) and I APPRECIATE A LOT your videos. Thanks to them we can approach a high level of problem resolutions as this one in which the irrational number i is used to get the solution. Congratulation and thank you for sharing with us your high level knowledge.
Or, in order to keep everything in integers for as long as possible, note that the middle coefficient is odd, so multiply by 4·6 (rather than by 6): 4·6·6x² - 24·7x = -24·8 12²x² - 2·12·7x = -192 12²x² - 2·12·7x + 7² = 49 - 192 (12x - 7)² = -143 x = (7 ± i√143)/12 Fred
Dumb question maybe but half of 2nd coefficient is 84, so don’t follow how you’re getting to 7squared instead of 84squared? Trying to relearn basic math to help my kids :). Thx.
6x^2-7x+8 =0, a= 6, b = -7, c = 8, -b = 7, b^2 = 49, 4ac = 4×6×8 = 192, b^2 -4ac = 48-192 = - 144 < 0 Since it is negative , this equation has no real roots.
For me it is very funny how you calculate the right side of the equation. You could do it like this: -4/3 + 49/144 = -192/144 + 49/144 = -143/144. Your way to do it seems like if a mountain hiker wants to reach the height of 1000 meters, so he goes up to 5000 meters and then comes down.
Excellent presentation. Thank you for this. I am now clarified that in finding a certain number to complete a square, we can possibly arrived on an imaginary number (ì). Kudos! Well explained.
You're very welcome Danny! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
@@BigWailz_official the solutions to ax^2 + bx + c = (-b +/- sqrt(b^2 - 4ac))/ 2a. This seems quite complicated, but once you use it a couple of times, you find that unless factorisation is very simple, it's the simplest method, and I always find it simpler than completing the square. It works all the time and you can also tell very simply how many real solutions there are based on whether the value in the square root is positive (2), zero (1) or negative (0).
Andy Wright that might be so, but the whole point of the video was to show that the completing the square method could be used - as his student had asked him. It does also bring in the concept of the imaginary number rather nicely and also builds on knowledge of splitting number to root them which is convenient too, for building in and reinforcing concepts covered in earlier lessons.
Hello, I think you could also use: 1) D= b Square - 4ac Knowing D is your discriminant! 2) - b + square root of D = x1 3) - b - square root of D = x2 What do you think?
Thank you so much King for your nice feedback. You are perfectly alright about the discriminant D= b Square - 4ac. I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃
This is so relaxing to the brain I feel loads just got lifted off my shoulders. I love getting a refresher on this; thanks very much for the link. It's been at least two years since I last did these equations.
May I suggest that when you combined the fractions, it would have been preferable to use the lowest common denominator, 144, rather than cross-multiplying, as this would lead to easier arithmetic with smaller numbers and avoid the need to cancel by sqrt(3) later.
Completing the square for this expression would be much better than beginning with the equation, as this also derives the coordinates for the vertex. If only roots are needed, then the formula is the obvious choice. Moreover, you should review adding fractions. -4/3 + 7^2/12^2 = -43/12^2. Only beauty lies in true mathematics.
You are very welcome Patel ji! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Thank you so much prakasam kannadi for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
I knew immediately that they were imaginary because the nature of the root (or the discriminatnt I.e. b^(2)-4ac) is less than zero so it must mean it has two imaginary solutions. Great video👍👍
Love the You Tube name you use. Reminds me of one of my favorite Adages. "Math is a Wonderful Thing. Become good enough at it, and no one will EVER be able to fool you with demagoguery." As for this video, my 8th grade algebra teacher took us through a drill very similar to this one. I raised my hand and asked "Wouldn't it be easier to just apply the Quadratic Equation?" He replied "With an attitude like that, you'd be better off becoming an Accountant than a Mathematician." So I did LOL All best!
In germany we have something that's called pq-Formel: when you see this equation x^2 + qx + q = 0, you can do this: X = - p/2 +/- Squarerootof [ (p/2)^2 - q]
When I was first looking at completing the square quadratics a few weeks ago, I stumbled across this video and it nearly blew my mind. I’ve studied a bit since and just rewatched it and bingo! Makes glorious sense now. Thank you 😊 But if you are a beginner to completing the square, start with a simple few examples that don’t involve fractions, to build your understanding first.
Dear Henry, you are absolutely correct! However, getting to know more tools and techniques would give you more power! I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃
The quadratic formula is the result of CTS. If you become proficient at CTS then you'll not only know where the quadratic formula came from, the quadratic formula becomes completely unnecessary. CTS is faster.
@ around 4:10 you put (7/12)^2 On both sides. later you said what sign to put in between x and 7/12 whole square... It wasnt necessary...you simply should have said...its taking on the form of a^2 - 2ab+b^2. And will so...reduce to (a-b) ^ 2 .That way it would have been simpler....
The steps would have been easier if you had just multiplied -4/3 by 48/48 (to get the 48, divide 144 by 3). Then if you are weak at fractions you could multiply both sides of the equation by 144.
I’m long out of math. Like these videos to refresh my mind. What is the purpose of completing the square? Knowing the formula I would never bother with this. Is their a reason to?
Since they have a common denominator, would you further simplify the solution as x = (7+i[143]^1/2)/12 and (7-i[143]^1/2)/12 ? Also, thank you for taking the time to show us this method. You have a very easy method of teaching that helps me to understand the material.
Dear Larry Patterson , you are absolutely correct. You may simplify it further. As a Math professor, I'd accept both versions of answers as perfectly alright. Thanks for the feedback. I'll be uploading many more video lessons pretty soon. Kind regards
Thanks sir This is my dad's phone .My teacher taught me this 5 five but i was not understanding .but yoday i saw ur video , u are fabulous I understood very fast
You're very welcome Umesh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
Great video for learners like us. But perhaps you forgot to tell the learners when you used the formula (a - b)^2 = a^2 - 2ab + b^2 in the LHS equation : x^2 - 7/6.x+ (7/12)^2 = ( x - 7/12 )^2. Instead, you brought down the negative sign before 7/12 by drawing an arrow. This confused me a little in the first hand. Thanks.
You are very welcome Earl! I'm sure you are very smart 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
In China,Chinese students learn Quadratic equation of one variable at the age of 14,but some Chinese students learn it at age of 10,11. This equation can be solved by complete squareformula or formula method.
Thanks to Po-Shen Lo (www.poshenloh.com/quadraticdetail/) the following is another elegant solution : If you find r and s with sum −B and product C, then x2+Bx+C=(x−r)(x−s), and they are all the roots • Two numbers sum to −B when they are −B/2±u • Their product is C when B2/4−u2=C • Square root always gives valid u • Thus −B/2±u work as r and s, and are all the roots So for the equation 6x2 - 7x + 8 = 0, we follow the following steps: Divide both sides by 6 resulting in x2 - 7/6x + 4/3 Two numbers that Sum to 7/6 are 7/12±u The product of the two numbers is (7/12 + u)(7/12-u)=4/3 Solving for you u as follows: 49/144-7u/12+7u/12-u2 = 4/3 49/144-u2 = 4/3 = 192/144 -u2 = 192/144 - 49/144 = 143/144 u2 = -143/144 u = (±i√143)/12 X = 7/12 (±i√143)/12
I've always felt that when you have to use "imaginary numbers" in your solution, that there is some fun gimmicky math to perform but there is no real solution. Kind of like yes we can travel to another galaxy - just let me fire up our imaginary space ship.
You wouldn't feel the same way, if we had another name for imaginary numbers. Like if we had called the number systems "direct numbers" and "lateral numbers" as Gauss had suggested. The name "imaginary numbers" makes it seem as if they lack real world application, but that is not correct at all. Math programs just don't bother teaching real word applications of imaginary numbers, because it takes another few years beyond high school to be ready to understand them. There are real world applications of imaginary numbers, such as keeping track of phase in AC electricity, or solving the differential equation of the oscillating mass on a spring.
Hi, thank you for your kind, helpful explanation, but I didn't understand why you divide the 2nd term (b term) by 2? Thank you, again . . . & God Bless . . .
Dear Glo Amador, you are very welcome. Thank you so much for taking the time to leave this comment. I'm sure you are an awesome student. Keep it up. Best regards :)
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Wonderful! Can we always take the half of coefficient number by 1\2...? And also can we also directly write the number obtained when multiplied by the coefficient number without making it smaller?
Shatha Omar He’s doing that so that we can write the left side as a perfect square, that’s one of the main steps regarding how to solve by ”completing the square”.
A machine can deal with this, so there's no intelligence needed just computation. This is high school algorithmic processing; there is no mathematics here just obscure trickery. This is why mathematics is difficult.
The smallest common multiple of the numbers 3 and 144 is the number 144. Why bring fractions to such a large denominator? With this approach, you do not need to reduce the fraction. Immediately get the irreducible fraction -143/144. The smaller the number, the fewer errors in the calculations.
Dear Jose Geonzon, here is the solution: solve by completing the square x^2+3x+2 = 0 => x^2+3x = -2 => x^2+3x +(3/2)^2= -2 +(3/2)^2 => (x + 3/2)^2 = -2 + 9/4 => (x + 3/2)^2 = 1/4 => take the square root on both sides and solve for x => x=-1, x=-2 are our solutions :) Thus, you can write your function f(x) = x^2+3x+2 as in this form as well => f(x) = (x + 3/2)^2 - 1/4. Thanks for asking. All the best :)
When completing the square, why do some RUclips Math teachers add the middle terms on the left hand side and to the right hand sides, while others minus the term they have just squared on the left hand side. You get two different answers, right. I just so confounded by which method to use. Please, help! Thank you 😃🤓
My daughter is using this mathematics to solve her assignment
Thanks for your help and support.
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Good . But what Is the meaning of each step . Why we add the steps that we wanted , there should be some meaning right
Plz watch
m.ruclips.net/user/Niteshsir
@@PreMath Why do you:
A. Pull the 7/6 aside and
B. Divide it by 2?
@@xsageonexx7399 Take, for example; x + b
Square it: (x + b)(x + b), and carry out the multiplication to get the product:
x^2 + 2bx + b^2
In the example polynomial, the 7/6 coefficient is your 2b, so you need to divide by 2, or multiply by 1/2 to get the value of b to add to the L-value to produce a perfect square.
I'm French. I'm retired (after a professional career in data processing). I love mathematics (it doesn't mean I'm an expert of it :-) and I APPRECIATE A LOT your videos. Thanks to them we can approach a high level of problem resolutions as this one in which the irrational number i is used to get the solution. Congratulation and thank you for sharing with us your high level knowledge.
9:16 When used as an operator, ± should be spoken as "plus or minus".
"positive or negative" is correct only when ± is used as a sign.
Yeah, contexts. Our teacher from math would note that, just like in your comment.
Or, in order to keep everything in integers for as long as possible, note that the middle coefficient is odd, so multiply by 4·6 (rather than by 6):
4·6·6x² - 24·7x = -24·8
12²x² - 2·12·7x = -192
12²x² - 2·12·7x + 7² = 49 - 192
(12x - 7)² = -143
x = (7 ± i√143)/12
Fred
0
ffggddss :thanks so much sir,your explanation is so clear
Genius
Now i got the point of denoting quadratic root of negative numbers. Thank you.
Dumb question maybe but half of 2nd coefficient is 84, so don’t follow how you’re getting to 7squared instead of 84squared? Trying to relearn basic math to help my kids :). Thx.
6x^2-7x+8 =0,
a= 6, b = -7, c = 8,
-b = 7,
b^2 = 49,
4ac = 4×6×8 = 192,
b^2 -4ac = 48-192 = - 144 < 0
Since it is negative , this equation has no real roots.
Именно так, и квадрат числа не может быть отрицательным, какой же тупой автор видео
For me it is very funny how you calculate the right side of the equation. You could do it like this: -4/3 + 49/144 = -192/144 + 49/144 = -143/144.
Your way to do it seems like if a mountain hiker wants to reach the height of 1000 meters, so he goes up to 5000 meters and then comes down.
Same thoughts! I'm really bothered with how he added the fractions 😂
Exactly.....
Excellent presentation. Thank you for this. I am now clarified that in finding a certain number to complete a square, we can possibly arrived on an imaginary number (ì). Kudos! Well explained.
You're very welcome Danny! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
Solving with the equation is much simpler
A=6, b=-7, c=8
X=(7+/-sqrt(49-4×6×8))/12
=(7+/-sqrt(49-192))/12
=7+/-sqrt(-143))/12
=7/12+/-sqrt(143)i/12
Thank you. This is correct
Please can you break down the simplification process so I can understand
@@BigWailz_official the solutions to ax^2 + bx + c = (-b +/- sqrt(b^2 - 4ac))/ 2a. This seems quite complicated, but once you use it a couple of times, you find that unless factorisation is very simple, it's the simplest method, and I always find it simpler than completing the square. It works all the time and you can also tell very simply how many real solutions there are based on whether the value in the square root is positive (2), zero (1) or negative (0).
Andy Wright that might be so, but the whole point of the video was to show that the completing the square method could be used - as his student had asked him.
It does also bring in the concept of the imaginary number rather nicely and also builds on knowledge of splitting number to root them which is convenient too, for building in and reinforcing concepts covered in earlier lessons.
Hello, I think you could also use:
1) D= b Square - 4ac
Knowing D is your discriminant!
2) - b + square root of D = x1
3) - b - square root of D = x2
What do you think?
Thank you so much King for your nice feedback.
You are perfectly alright about the discriminant D= b Square - 4ac.
I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃
you must answer the question as written
D= -
This is so relaxing to the brain I feel loads just got lifted off my shoulders. I love getting a refresher on this; thanks very much for the link. It's been at least two years since I last did these equations.
Anyone teaching equation should explain the rules........ Whenever someone understands the rules, everything becomes easy.
The rules?
Pure bs dreamt up by some arab this shit is out dated
May I suggest that when you combined the fractions, it would have been preferable to use the lowest common denominator, 144, rather than cross-multiplying, as this would lead to easier arithmetic with smaller numbers and avoid the need to cancel by sqrt(3) later.
Completing the square for this expression would be much better than beginning with the equation, as this also derives the coordinates for the vertex. If only roots are needed, then the formula is the obvious choice. Moreover, you should review adding fractions. -4/3 + 7^2/12^2 = -43/12^2. Only beauty lies in true mathematics.
Thanks dear for the nice feedback. I really appreciate that.
Take care dear and all the best😃
Have a very happy and blessed New Year!
You cannot take Square root of an expression. It has to be in simplified form. Else it should be in Modulus.
Thank you so much for your explanation. I'm from India 🇮🇳but I can understand your explanation comletely.👍
You are very welcome Patel ji! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Please make a video on real life use of limits , mathematical induction,complex numbers
Step by step approach to answer is simply super.
Thank you so much prakasam kannadi for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
Subscribed! Great explanation!
Thank you so much! Please keep supporting my channel. Kind regards 😀
I knew immediately that they were imaginary because the nature of the root (or the discriminatnt I.e. b^(2)-4ac) is less than zero so it must mean it has two imaginary solutions. Great video👍👍
hahaha who cares fucking knowitall hahaha
Gauss.
lol
luis portella You can’t comprehend such low level math? Hahaha.
Good professor 🌷💐🌺🌺💐
Thanks and welcome
Thank you so much I was able to challenge some people
Great video. As a math teacher myself, I love how you skipped no steps.
MathGives YouPower , thanks for the honest feedback. We both are in this very noble teaching profession. Kind regards :)
Love the You Tube name you use. Reminds me of one of my favorite Adages. "Math is a Wonderful Thing. Become good enough at it, and no one will EVER be able to fool you with demagoguery."
As for this video, my 8th grade algebra teacher took us through a drill very similar to this one. I raised my hand and asked "Wouldn't it be easier to just apply the Quadratic Equation?" He replied "With an attitude like that, you'd be better off becoming an Accountant than a Mathematician." So I did LOL
All best!
where did the 7/12 and 2/1 come from? I think I have frozen my brain. I love math; this has me stumped. I would make my dad, the math prof so proud :)
In germany we have something that's called pq-Formel: when you see this equation x^2 + qx + q = 0, you can do this: X = - p/2 +/- Squarerootof [ (p/2)^2 - q]
You kan simply solve it with
(X= -b + and - √b squar - 4ac all over 2a, a as 6 ,b as -7 ,c as 8
Mustafa Sleiman that’s not fun
That’s not what his student asked him to do.
We can ×6# 36 x^2_42x+48=0 then (6x_7/2)^2=_47/2
If ax2+bx+c =0, the solution of formula is -b+-✓ b2-4ac（radical symbol)/2a.
Exactly right
Content - can you solve this
Me - No, that's why I am going to see this video
Legends - No, and I don't need to 🤣
When I was first looking at completing the square quadratics a few weeks ago, I stumbled across this video and it nearly blew my mind. I’ve studied a bit since and just rewatched it and bingo! Makes glorious sense now. Thank you 😊
But if you are a beginner to completing the square, start with a simple few examples that don’t involve fractions, to build your understanding first.
You are very welcome Lottie Bronte! Glad I could help you. Thanks for your comments. Please keep supporting my channel. Take care😃
Yes I can but why should I when using the quadratic formula is so much easier?
Dear Henry, you are absolutely correct! However, getting to know more tools and techniques would give you more power!
I'm sure you are an awesome student 👍 Please keep sharing my channel with your family and friends. Take care dear and all the best😃
The question asked specifically for this method - in an exam you would lose marks for ignoring that
The quadratic formula is a generalized form of completing the square. Good to know that because I'm always forgetting the damn formula.
The quadratic formula is the result of CTS. If you become proficient at CTS then you'll not only know where the quadratic formula came from, the quadratic formula becomes completely unnecessary. CTS is faster.
@ around 4:10 you put (7/12)^2 On both sides. later you said what sign to put in between x and 7/12 whole square...
It wasnt necessary...you simply should have said...its taking on the form of a^2 - 2ab+b^2. And will so...reduce to (a-b) ^ 2 .That way it would have been simpler....
Explanation was very good. You please shutup
You are correct.
This is to help me refreshing for my daughter’s pre calculus . Thank you very much !!!!
@5:39 in video (-429/432) reduces to -(143/144)
johnnie gilkerson hahaha, exactly
3 is a factor of 144. You only needed to multiply -4/3 by 48/48 and then add with 144 denominator. You could have saved steps there
The steps would have been easier if you had just multiplied -4/3 by 48/48 (to get the 48, divide 144 by 3). Then if you are weak at fractions you could multiply both sides of the equation by 144.
I was also thinking the same
I’m long out of math. Like these videos to refresh my mind.
What is the purpose of completing the square? Knowing the formula I would never bother with this. Is their a reason to?
hahaahahahahahaha great question. well i guess teachers want us to fail, thats why
it can help with maximums
I know this method and this method is given in book examples
Thats what people dnt understand. Actually i ve to use that method for my hw.
Since they have a common denominator, would you further simplify the solution as x = (7+i[143]^1/2)/12 and (7-i[143]^1/2)/12 ? Also, thank you for taking the time to show us this method. You have a very easy method of teaching that helps me to understand the material.
Dear Larry Patterson , you are absolutely correct. You may simplify it further. As a Math professor, I'd accept both versions of answers as perfectly alright. Thanks for the feedback. I'll be uploading many more video lessons pretty soon. Kind regards
Larry Patterson hi
Larry. I did this problem with my algebra class and then we watched the video together. Like you, we further simplified the final answer.
1:28 "The next thing what we want to do" ... I'm so glad this isn't an English lesson ... "isn't it".
Thanks sir This is my dad's phone .My teacher taught me this 5 five but i was not understanding .but yoday i saw ur video , u are fabulous I understood very fast
You're very welcome Umesh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
What happened to the -7/6x?
So best and great video but l am daily using video wow amazing sir l like you video
Exam be like: this is a 2 mark question
Lol
Thank you
Thank you so much! Please keep supporting my channel. Kind regards 😀
Great video for learners like us. But perhaps you forgot to tell the learners when you used the formula (a - b)^2 = a^2 - 2ab + b^2 in the LHS equation : x^2 - 7/6.x+ (7/12)^2 = ( x - 7/12 )^2. Instead, you brought down the negative sign before 7/12 by drawing an arrow. This confused me a little in the first hand. Thanks.
Exactly! I had the same confusion for a little while, too.
You explain very well👍
That's the method every student should master. Thanks.
6x^2 - 7x = --8
6x(x--7) = --8
Choose the right one from
1 x --8
--1 x 8
2 x --4
--2 x 4
and find value of X
Thanks Anjaneya for your awesome feedback!
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In electronic engineering, " i " is replaced with " j ". The reason for that is, lower case " i " is the current symbol in AC circuits.
Multiply 6x^ by 8
thank you for this. i thought i'd never learn this, but thanks to your wisdom and clarity in explaining, i was able to do my cousin's hw
You are very welcome Earl! I'm sure you are very smart 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
In China,Chinese students learn Quadratic equation of one variable at the age of 14,but some Chinese students learn it at age of 10,11.
This equation can be solved by complete squareformula or formula method.
No doubt Chinese kids are smart!
Thanks for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regard
Just solve for x to the first power and iteratively solve.
Thanks to Po-Shen Lo (www.poshenloh.com/quadraticdetail/) the following is another elegant solution
:
If you find r and s with sum −B and product C, then x2+Bx+C=(x−r)(x−s), and they are all the roots
• Two numbers sum to −B when they are −B/2±u
• Their product is C when B2/4−u2=C
• Square root always gives valid u
• Thus −B/2±u work as r and s, and are all the roots
So for the equation 6x2 - 7x + 8 = 0, we follow the following steps:
Divide both sides by 6 resulting in x2 - 7/6x + 4/3
Two numbers that Sum to 7/6 are 7/12±u
The product of the two numbers is (7/12 + u)(7/12-u)=4/3
Solving for you u as follows:
49/144-7u/12+7u/12-u2 = 4/3
49/144-u2 = 4/3 = 192/144
-u2 = 192/144 - 49/144 = 143/144
u2 = -143/144
u = (±i√143)/12
X = 7/12 (±i√143)/12
You are excellent ,that is the way I learned by doing all the steps.
Really - b+-root over b square - 4@c / 2a simple why to do this much and gone to pit of gutter
Sankalp Nagar because they have to do it that way
I've always felt that when you have to use "imaginary numbers" in your solution, that there is some fun gimmicky math to perform but there is no real solution. Kind of like yes we can travel to another galaxy - just let me fire up our imaginary space ship.
You wouldn't feel the same way, if we had another name for imaginary numbers. Like if we had called the number systems "direct numbers" and "lateral numbers" as Gauss had suggested. The name "imaginary numbers" makes it seem as if they lack real world application, but that is not correct at all.
Math programs just don't bother teaching real word applications of imaginary numbers, because it takes another few years beyond high school to be ready to understand them. There are real world applications of imaginary numbers, such as keeping track of phase in AC electricity, or solving the differential equation of the oscillating mass on a spring.
Galaxy math
L.C.M.of 3 and 144 is 144 so -4x48+ 49 gives -143/144
Thank you.
You're welcome!
Thanks you sir for this video i got 5/5in my test of this topic thank you soo much ❤❤❤❤
Most welcome 😊
@@PreMath why in 2:20 you had to divide by 2/1
Hi, thank you for your kind, helpful explanation, but I didn't understand why you divide the 2nd term (b term) by 2? Thank you, again . . . & God Bless . . .
. . . oops, never mind, Sir . . . I just found the answer in one of your other super-great videos . . . Thank you so, so much, &, God Bless . . . :)
Dear Glo Amador, you are very welcome. Thank you so much for taking the time to leave this comment. I'm sure you are an awesome student. Keep it up. Best regards :)
I hate competing the square and by the way this absolutely helped me
At the beginning only you can use the formula as x=(-b±√(b^2-4ac))/2a
There is a : x² 1x = (x - ½)² - 1²/4 that is pretty easier ..
Pretty good video. [(x - 7/12)(x - 7/12)] + (143/144) = 0 is the way I was taught that you leave it.
X=squareroot of 7x-4 OVER 3
Very clear to me as a student... Tnx
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If you want to make surface spread there are two solutions for I. An upper curve and a lower one.
Just subscribed ! You are a life saver
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very good explanation... you are really good teacher and not for duffers like some of those who commented below....
Very well explained! Would using the quadratic formula result in the same answers?
Wonderful! Can we always take the half of coefficient number by 1\2...? And also can we also directly write the number obtained when multiplied by the coefficient number without making it smaller?
I mean can we always multiply the coefficient number by 1\2
with i²=-1 it is wunderfull
need more explanation because why should we take square of 7/2. There is logic behind and this logic should be explain. good effort
Same answer with the quadratic formula
Very very good
Very nice
Super super
Well done sir but you made it long instead of short
Good explication. Thanks
I love solving questions like this
Pretty good sir! Best explainer
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Thank you for all this great knowledge
Why did you take the number 7/6 and multiply or divided it by half n then put exponents 2?? Could not get this step plz
7x/12+7x/12=14X/12=7x/6
Shatha Omar He’s doing that so that we can write the left side as a perfect square, that’s one of the main steps regarding how to solve by ”completing the square”.
144 and 3 have a lower common multiple 144
A machine can deal with this, so there's no intelligence needed just computation. This is high school algorithmic processing; there is no mathematics here just obscure trickery. This is why mathematics is difficult.
Thank you.... thank you soooo very much sir......I was facing prblm in this thing for many days....
Thanks for clearing my doubt.........😊
Good thanks
Thank you too!
Why did you divide 7/6 by 2? Please clarify.
It can be solved by using Middle Term Spilitting also
I wish math class never existed. Math too hard to me :(
there is practicle math' then there is nonsense math as above .........
Yep, junior high school maths nightmare coming to haunt me tonight
The smallest common multiple of the numbers 3 and 144 is the number 144. Why bring fractions to such a large denominator? With this approach, you do not need to reduce the fraction. Immediately get the irreducible fraction -143/144. The smaller the number, the fewer errors in the calculations.
Why can’t I use the method you taught, by doing (6x+1)(6x-8) and x = -1/6, or x _ 4/3?
(6x-1)(6x+8) isnt equal to 6x²-7x+8
Why to fill c ( notation a, b and c) was b divided 2, where was 2 come from?
Thank you
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@@PreMath thank you so much
Sir can you answer this one, f(x) = x^2+3x+2 by completing the square
Dear Jose Geonzon, here is the solution:
solve by completing the square x^2+3x+2 = 0 => x^2+3x = -2 =>
x^2+3x +(3/2)^2= -2 +(3/2)^2 => (x + 3/2)^2 = -2 + 9/4 => (x + 3/2)^2 = 1/4 => take the square root on both sides and solve for x => x=-1, x=-2 are our solutions :)
Thus, you can write your function f(x) = x^2+3x+2 as in this form as well
=> f(x) = (x + 3/2)^2 - 1/4. Thanks for asking. All the best :)
Multiply 6 by all the coefficients, then use the common sentence, then simplify the parentheses that can be simplified by 6.Why these long methods
Thanks Amin for you nice feedback.
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Omg 😳
I read that General Omar Bradley used to like to solve these types of equations to relax. Me math gave me a huge headache.
Get more from here: ruclips.net/video/xNghsdA7nag/видео.html
Divide:(12x^4-15x^3)÷3x^2 please
When completing the square, why do some RUclips Math teachers add the middle terms on the left hand side and to the right hand sides, while others minus the term they have just squared on the left hand side. You get two different answers, right. I just so confounded by which method to use. Please, help! Thank you 😃🤓
You can use any method
Thank you so much
Good
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@@PreMath ok my frand
Amazing Good
Well done
Thank u sir
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