Excellent explanation. What makes it so clear is that you "factor" the modified expression to show exactly why the 25 is in there. Most people don't include that part in the explanation. Understanding how and why is so much better than trying to memorise a series of stages that make no sense without context. Thank you.
Thank you so much!! I looked at like 5 different videos and none of them made any sense to me until this one!! All of the others just beat around the bush and did some weird method that took like ten minutes. I wished I could give 20 thumbs ups. You've got a new subscriber!
THANK YOU! This helped me so much with studying for a test. No other video explained it like this and i was completely clueless. You explained it so well and made it so much easier to understand!!
Great explanation! One thing I would add at the end. 32 is 16 * 2. Therefore, after the plus and minus we can put four times the square root of 2. That would be in a more simplified form.
You breaking it down is beautiful, thanks for the help. You're an angel! you didn't leave anything out and you answered ALL my questions thoroughly. sorry I'm 8 years late lol
Check out Mind Your Decision's explanation of quadratics using geometry. It visually shows "completing the square" making it concrete why you take half of b and square it. Really neat way to see it. This was still very good. Putting the two together is helpful.
THANK YOU. Geezus. I'm a grown adult taking a business math class, and I'd forgotten how to factor that out. After two days of watching videos and reading books, this finally clicked for me. Thank you thank you thank you.
Completing The Square really makes sense when you see it done with the area model. It because obvious why the middle term is divided in 2 and squared. A Quadratic is a square, geometrically-speaking. The reason you divide the middle term in 2 is because each side lengths have to be the same. You square it because you are literally adding a missing square units (length X width) to the larger square to make it whole. One thing I've learned about math is the more you understand (concepts and mathematical logic), the less you have to memorize. Math is just the language of numbers. Good luck in school.
They say a topic isn’t fully understand until the person can teach it, yep, this guy understands it, makes it look oh so simple 🙀🙀😳😩, is a really good video..
@@stuartbowman_ Oh my gosh, I had thought you left, your tutoring level is so much better then anyone I find on youtube and they try to make it look cool with graphics but you doing it on paper really makes it feel like authentic maths! I wish you would come back
could you do a video about rational functions, equations, and inequalities i'm having a hard time dealing with complicated problems but you're videos always helps out. thank you very much :)
My gods. I was so confounded as to why we were doing all that stuff to b in ax^2+bx+c=0. I don't know how i didn't recognize the perfect square before! Why do so many math courses insist on just telling you how to get the right answer without explaining how it works or what the underlying concept is?! It makes so much sense now. I'm ashamed for not realizing it all right away. I wish i could give this video more than one thumbs up. My gods...
twistedblktrekie I've been homeschooling myself alone with books and online resources for over a year now. The internet and myself are the best teachers i've ever had. Math teachers would practically never explain anything. I went to a public school in a ghetto too, so, that also probably didn't help. I can hardly wait until i start calculus. I never imagined that i would actually love mathematics.
twistedblktrekie I learn in a similar way, but for me, if it doesn't make sense to me conceptually, i'll have more trouble recalling it, and i'll get frustrated, so, i usually don't move on until i understand the concept adequately at the very least (by my own judgement i suppose, but hey). Luckily, the concepts often aren't difficult for me to understand at all, but i'm only on algebra 2 right now. I desperately want to be a physicist. I don't know if i can, or if i can even get into a good university due to my past and the circumstances my past has put me in. But it's what i want anyway. I'm 19, so i'm already very behind too.
twistedblktrekie My mom is a nurse; knowing what i know, i would never ever get into medical. Physics is my dream. It has been since 1st grade. I'm just not giving up because there isn't much else i want out of life aside from that anyway, aside from my dogs and some video games. Money doesn't matter much to me as long as i have those 3 things and sustenance, basically.
twistedblktrekie Honestly, i only took half a course in quantum mechanics before i decided to stop and go learn the math first. But, that half a course changed the world in my eyes, and i feel like it's something i'd like to put my life into. I loved physics since first grade; i just didn't know it before about a year and a half ago. There are a lot of good physics courses online, and a lot of good books if you're interested. I personally would recommend the Feynman lectures firstly. Wish me luck... I'll probably have a hard time getting into a good university, but, i suppose i'm too dense to give up.
twistedblktrekie It depends. There are jobs in universities, in companies, and for the government. The university jobs are the best; and the most difficult to attain. I do not want to work for the government, but company jobs can vary greatly. I want to be able to do actual research though. I really need to get into a top school, at least for grad school. People who go to just any old university for a physics major seem to always end up in a cubicle farm doing work that their heart isn't in.
OMGGGG THANK YOU IVE BEEN STUCK WITH THIS FOR 9HRS BUT NOW I UNDERSTAND GOD BLESS YOU I WAS ABOUT TO CHECK YOUR OTHER VIDEOS BUT YOU ONLY HAVE *VIDS WE NEED MORE PEOPLE LIKE YOUUUUUUU AAAA THANKASSASAS
@@user-in9of6os2c ... yes... you have to move the end coefficient to the other side in order to make a perfect square on one side... but also note you have to add the new coefficient to both sides in order for the equation to balance. As you can see, he’s not done anything that unbalances the equation. Eg, he hasn’t added to one side, that he hasn’t done for the other... I hope that helps. The formula he gave is ‘B (middle coefficient of x) divided by 2 and squared’. So, half of 10 and squared = 25... then add 25 to both sides. Also remember, X is one side of the equation and Y is the other... on your graph, you have X axis, positive & negative, and Y axis, positive and negative.... thus a squared graph, and why the expression is completing the square. After you’ve solved the quadratic equation, for X & Y, you can then plot or plug in the numbers onto your graph... it looks hard, but when you know how and why it’s used, it’s actually a work of genius.
This is the most rationale explanation I have seen. Moreover, the narrative can be said to be measured, natural and straight to the point. Impressive way of reassuring learners whilst going through the steps in a clear and humble manner. In short, the video is about the subject and not about 'creating a personality or show' to pseudo entertain. Love this method of calm step by step explanation.Could there be a similar video, but of the type where the x squared term has a leading co-efficient?
Great to hear, thanks man. No I don't have any videos specifically about that, but you can always divide both sides of the equation by whatever the leading coefficient is to eliminate it. If you proceed from there with the same method, it won't be pretty but it'll work. Cheers
Thank you SO much. I am studying for my CSET and this is the only one that breaks it down the way that makes sense. I couldn't figure out what the point was in using Completing the Square when we can factor or use the Quadratic Equation. Other channels say "If a is equal to 1, add b/2 squared and it completely threw me off. But, what if a is not equal to 1?
dude, thank you SO much! i was having a hard time with this and this totally helped! bonus points for also actually explaining how and why it works the way it does!
Thank you for taking the time to explain each step (even the "dumb" ones). Other videos we watched on this subject glossed over the "obvious" steps, making them impossible to follow (giving me flashbacks to some of the really bad math teachers I've had). My son was able to complete his math homework, thanks to you!
I can think of factors that multiply to give -7 and add to give 10: 5 + sqrt(32) 5 - sqrt(32) The point being, just cause something can't be factored using integers, it doesn't mean it can't be factored.
Thanks - very useful -- normally that '25' that you put in is put in as a fraction over 2, then brackets which are squared ... exactly the same thing, but o much more confusing when you don't really realise what's happening to/with that extra equation - this made it crystal clear :)
I'm looking at the comments in a bunch of videos and all these people seem like they are in a higher grade than me doing what I'm doing. I'm in 8th grade? What? I'm home schooled but someone pls answer my question. Why is this happening to me. Okay I'm done (btw u r better than my teacher)
Happy to see a teacher that can actually teach. Most teachers on youtube, or even at schools, do not know how to explain to students.
Excellent explanation. What makes it so clear is that you "factor" the modified expression to show exactly why the 25 is in there. Most people don't include that part in the explanation. Understanding how and why is so much better than trying to memorise a series of stages that make no sense without context. Thank you.
Deffinetly better than ur prof , straight to the point . It feels like a private lesson 😂😂😂
i have also explained this method in more easily .. watch on my youtube channel .. Tajamul Sir ..
I’ve just had a private lesson ,and still can’t do it
OH MY GOD THANK YOU. All the other videos didn’t make any sense. Bless your soul. Your username is true.
Hey
100% agreed thx so much BetterThanYourProf
You actually are better than all the professors I've had combined.
Thank you so much!! I looked at like 5 different videos and none of them made any sense to me until this one!! All of the others just beat around the bush and did some weird method that took like ten minutes. I wished I could give 20 thumbs ups. You've got a new subscriber!
why is this 480p vid lookin lik a 1080p one?
yup it looks like one
Shhhs dont complain,YT might screw us over if the find out
Simple colour palette, nothing to blur.
Haha I actually filmed this on my super old Droid RAZR. I really don't get it either :D
THANK YOU! This helped me so much with studying for a test. No other video explained it like this and i was completely clueless. You explained it so well and made it so much easier to understand!!
U r actually better than my prof😂😂
LOL
Great explanation! One thing I would add at the end. 32 is 16 * 2. Therefore, after the plus and minus we can put four times the square root of 2. That would be in a more simplified form.
You breaking it down is beautiful, thanks for the help. You're an angel! you didn't leave anything out and you answered ALL my questions thoroughly. sorry I'm 8 years late lol
i love it. i like how you explain things so gentle for us to understand better thankyou
This video had all the steps explained carefully and well. It has really really helped me. THANK YOU !
There’s five methods actually...
Isolation
Quad formula
Diamond
Complete the square
Grouping
6. Giving up
@@benisman underrated comment
@@ayushkishor3207 for real
I just want 3 it's too much for me
Summer class Gaming WOAH TWO YEARS AGO LOL quadratics are easy as you get higher and higher in math
BEST EXPLANATION EVER♥️
Bruh this guy is a genius he deserves more subs
Check out Mind Your Decision's explanation of quadratics using geometry. It visually shows "completing the square" making it concrete why you take half of b and square it. Really neat way to see it.
This was still very good. Putting the two together is helpful.
Thank you so much! I've watched so many videos and this was the only one that made sense! Thank yooooooou
Dude, you are literally a legend! tysm for the clear explanation, the best I could find on YT so far!
this video is 9 years old, wow i hope this person is doing well in life and im wishing them the best
I'm good :) So glad these videos are still useful to people
@@stuartbowman_ OHMYGOD,,, you replied! glad to hear that! and yes this was very helpful, thank you so much!
THANK YOU. Geezus. I'm a grown adult taking a business math class, and I'd forgotten how to factor that out. After two days of watching videos and reading books, this finally clicked for me. Thank you thank you thank you.
Completing The Square really makes sense when you see it done with the area model. It because obvious why the middle term is divided in 2 and squared. A Quadratic is a square, geometrically-speaking. The reason you divide the middle term in 2 is because each side lengths have to be the same. You square it because you are literally adding a missing square units (length X width) to the larger square to make it whole. One thing I've learned about math is the more you understand (concepts and mathematical logic), the less you have to memorize. Math is just the language of numbers. Good luck in school.
They say a topic isn’t fully understand until the person can teach it, yep, this guy understands it, makes it look oh so simple 🙀🙀😳😩, is a really good video..
what happens when your "B" value doesn't give a good number when dividing by 2? For example, what if the B value is 15 or 9 or 33?
Seeing this video after 10 years but then also a life saver and by following the rules of algebra, this equates this video to a legend
#THANKS BRO#
Oooh so good!!!! Even at my higher level of study I still had issues but these video has helped me
So far I'm now good!!
The best explanation so far
Dude the way you teach is fantastic… you really give thought to what some people may or may not know! Thank you so much!
Thanks! Back when I made these videos I was tutoring math every day so I had lots of practice
@@stuartbowman_ Oh my gosh, I had thought you left, your tutoring level is so much better then anyone I find on youtube and they try to make it look cool with graphics but you doing it on paper really makes it feel like authentic maths! I wish you would come back
Best explanation on RUclips. I remember being confused on this when I was in 10th grade.
Your lecture is quite intelligible, I'm very glad, thank you
I know this is a relatively old video, nonetheless, I found it very helpful and was finally able to connect some concepts. Thank you.
heh
could you do a video about rational functions, equations, and inequalities i'm having a hard time dealing with complicated problems but you're videos always helps out. thank you very much :)
BRO, thank you! you saved me from getting a 1 hour detention!
you definitely better than my prof thaaaaaaaaaaaaaaannnnnnkkk yoooooooooooouuuuuuuuuuu
That is the best explanation of completing the square I've heard. Bless you sir!
My gods. I was so confounded as to why we were doing all that stuff to b in ax^2+bx+c=0.
I don't know how i didn't recognize the perfect square before!
Why do so many math courses insist on just telling you how to get the right answer without explaining how it works or what the underlying concept is?!
It makes so much sense now. I'm ashamed for not realizing it all right away.
I wish i could give this video more than one thumbs up.
My gods...
twistedblktrekie I've been homeschooling myself alone with books and online resources for over a year now. The internet and myself are the best teachers i've ever had.
Math teachers would practically never explain anything. I went to a public school in a ghetto too, so, that also probably didn't help.
I can hardly wait until i start calculus. I never imagined that i would actually love mathematics.
twistedblktrekie I learn in a similar way, but for me, if it doesn't make sense to me conceptually, i'll have more trouble recalling it, and i'll get frustrated, so, i usually don't move on until i understand the concept adequately at the very least (by my own judgement i suppose, but hey).
Luckily, the concepts often aren't difficult for me to understand at all, but i'm only on algebra 2 right now.
I desperately want to be a physicist. I don't know if i can, or if i can even get into a good university due to my past and the circumstances my past has put me in. But it's what i want anyway. I'm 19, so i'm already very behind too.
twistedblktrekie My mom is a nurse; knowing what i know, i would never ever get into medical. Physics is my dream. It has been since 1st grade. I'm just not giving up because there isn't much else i want out of life aside from that anyway, aside from my dogs and some video games. Money doesn't matter much to me as long as i have those 3 things and sustenance, basically.
twistedblktrekie Honestly, i only took half a course in quantum mechanics before i decided to stop and go learn the math first. But, that half a course changed the world in my eyes, and i feel like it's something i'd like to put my life into. I loved physics since first grade; i just didn't know it before about a year and a half ago.
There are a lot of good physics courses online, and a lot of good books if you're interested. I personally would recommend the Feynman lectures firstly.
Wish me luck... I'll probably have a hard time getting into a good university, but, i suppose i'm too dense to give up.
twistedblktrekie It depends. There are jobs in universities, in companies, and for the government. The university jobs are the best; and the most difficult to attain. I do not want to work for the government, but company jobs can vary greatly. I want to be able to do actual research though.
I really need to get into a top school, at least for grad school. People who go to just any old university for a physics major seem to always end up in a cubicle farm doing work that their heart isn't in.
THANK YOU SO MUCH. Your video was the only one that made any sense at all. You put Khan Academy to shame! ;) God bless you!!
You have no idea how much I love you
OMGGGG THANK YOU IVE BEEN STUCK WITH THIS FOR 9HRS BUT NOW I UNDERSTAND GOD BLESS YOU I WAS ABOUT TO CHECK YOUR OTHER VIDEOS BUT YOU ONLY HAVE *VIDS WE NEED MORE PEOPLE LIKE YOUUUUUUU AAAA THANKASSASAS
You're welcome! Glad it made sense
Glad I could help
I just have one thing to ask why did you cancel the -7?
And like would that happen in like any question with completing the square
@@user-in9of6os2c ... yes... you have to move the end coefficient to the other side in order to make a perfect square on one side... but also note you have to add the new coefficient to both sides in order for the equation to balance. As you can see, he’s not done anything that unbalances the equation. Eg, he hasn’t added to one side, that he hasn’t done for the other... I hope that helps. The formula he gave is ‘B (middle coefficient of x) divided by 2 and squared’. So, half of 10 and squared = 25... then add 25 to both sides. Also remember, X is one side of the equation and Y is the other... on your graph, you have X axis, positive & negative, and Y axis, positive and negative.... thus a squared graph, and why the expression is completing the square. After you’ve solved the quadratic equation, for X & Y, you can then plot or plug in the numbers onto your graph... it looks hard, but when you know how and why it’s used, it’s actually a work of genius.
This is the most rationale explanation I have seen. Moreover, the narrative can be said to be measured, natural and straight to the point. Impressive way of reassuring learners whilst going through the steps in a clear and humble manner. In short, the video is about the subject and not about 'creating a personality or show' to pseudo entertain. Love this method of calm step by step explanation.Could there be a similar video, but of the type where the x squared term has a leading co-efficient?
Great to hear, thanks man. No I don't have any videos specifically about that, but you can always divide both sides of the equation by whatever the leading coefficient is to eliminate it. If you proceed from there with the same method, it won't be pretty but it'll work. Cheers
Im south africa and ive just subscribed and pressed d alert button. U d best man. Better dan those plastic professors LOL
You are the best mathermatics teacher
Thanks for sharing your knowledge.
This is very helpful and easy to understand.
Thank you!! Got straight to the point and was very informative :)
Thank you SO much. I am studying for my CSET and this is the only one that breaks it down the way that makes sense. I couldn't figure out what the point was in using Completing the Square when we can factor or use the Quadratic Equation. Other channels say "If a is equal to 1, add b/2 squared and it completely threw me off. But, what if a is not equal to 1?
Then you divide all the numbers by the a
FOR example 2x² + 10x = 0
You do 2x²/2 + 10x/2 = 0
i literally watched 40 videos prolly but this one is the only one i understood by watching it ONCE
your S's sound like a blow off valve, good video clears all of the confusion i had up.
dude, thank you SO much! i was having a hard time with this and this totally helped! bonus points for also actually explaining how and why it works the way it does!
Your video really helped me I appreciate it thanks 🙏
√32 is reducible to 4√2.
I was wondering about that. Is it considered incorrect if the reduction is not completed?
@@leonelfederico245 i dont know
@@leonelfederico245 it's considered incorrect.
Thank you for taking the time to explain each step (even the "dumb" ones). Other videos we watched on this subject glossed over the "obvious" steps, making them impossible to follow (giving me flashbacks to some of the really bad math teachers I've had). My son was able to complete his math homework, thanks to you!
"I can't think of any factors of 7..." It's a prime number!
@Matthew Bair Yeah, that' a Prime number.
I'm so slow at learning this kind of stuff but when I saw this I got it straight away
Amazing job man you did a great job and helped me a lot
Thanks for making the concept clear! You're a great teacher..
finding this video is the highlight of my quarantine
This really IS the best explanation!!
u are definitely surely amazingly better than my prof hat on you
Thanks, You saved my life. Got yourself a new sub
Literally the best explanation
watched so many videos, this is the one that made me finally get it so thank you!
I can think of factors that multiply to give -7 and add to give 10:
5 + sqrt(32)
5 - sqrt(32)
The point being, just cause something can't be factored using integers, it doesn't mean it can't be factored.
Thanks - very useful -- normally that '25' that you put in is put in as a fraction over 2, then brackets which are squared ... exactly the same thing, but o much more confusing when you don't really realise what's happening to/with that extra equation - this made it crystal clear :)
That is the best explanation I have seen. Thanks.
Im from the Philippines
Good explanation bro
The actual process is divide all terms by the coefficient of the x^2 before proceeding to the process explained.
Best explanation ever♥️
This was Extremely helpful! thanks a ton!
My mind just got a workout! Well explained.
Your explaining very cleanse..
Great vid man, really helped me out can you do more?
where was youtube when i was in highschool in the 80s
Title is accurate. Thumbs up
Awesome Explanation!!! Thank you so much 🙏
Well done, clear process and clear easy to follow notes.
If the leading coefficient is > or = 2, how would I go about solving the equation? Say 3x^2 - 12x + 9
Bro ur literally the best
Love the way you teach❤❤❤❤
what if you had an equation where you have to divide by a negative like -4b=64
you sir, are a GOD
Thank you im in 8th grade and learning algebra my teacher doesn't explain it like you do.
What if the linear term is negative when we are going to found the square root of it.Can I square root it even it's negative?
It make sense thanks for sharing your ideas.
this was very helpful ^.^
Someone else needs a math channel called "In plane english"
We could further simplify it as
-5 ± sqrt16 × sqrt2
-5 ± 4sqrt2
5:36 why is it -5 and how do you know when to make it -
OH Thank you BetterThanYourProf :)
It help my homework :)
Actually better than my prof😂😂
Informative
For a demo, why didn't you start with x^2 + 10x - 11 = 0 ? That way, after completing the square, you get a perfect square on each side.
better than our math teacher
lol my teacher explained the exact same thing but i only understood this one for some reason xD. Thanks this was helpful.
Awsome explanation
Why does 1/2 of the coefficient of x suddenly come into the equation? What role does it play in it?
I'm looking at the comments in a bunch of videos and all these people seem like they are in a higher grade than me doing what I'm doing. I'm in 8th grade? What? I'm home schooled but someone pls answer my question. Why is this happening to me. Okay I'm done (btw u r better than my teacher)
Można także to równanie kwadratowe rozwiązać przy pomocy delty .
Doesnt radical 32 simplify in 4radical2
Yes.
Leaving sqr32 in math tests is unacceptable in my country. Should be sqr 16*2 = 4 sqr2.
BTW.
This quadratic equation might be figured way easily:
1/ Delta = b^2 - 4ac = 128
2/ sqr 128 = 4 sqr8
3/ x1 = -5 - 2 sqr8
X2 = -5 + 2 sqr8
Eot