How to Solve By Completing the Square (NancyPi)
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- Опубликовано: 2 авг 2024
- MIT grad shows the easiest way to complete the square to solve a quadratic equation. To skip ahead: 1) for a quadratic that STARTS WITH X^2, skip to time 1:42. 2) For a quadratic that STARTS WITH 2X^2, 3X^2, etc., skip to time 6:46. 3) For NEGATIVE leading term like -X^2, skip to 13:34. 4) If there's NO X TERM (ex. 3x^2 - 121 = 0), then you cannot complete the square and can solve directly - skip to 16:30. Nancy formerly of MathBFF explains the steps.
Follow Nancy on Instagram: / nancypi
Twitter: / nancypi
How to complete the square when solving quadratic equations:
Completing the square means re-arranging the quadratic equation into the neat, "perfect square" form (x + number)^2 equals another number, or (x - number)^2 equals another number. The point of doing this is so that you can solve by just square-rooting both sides of the equation.
If your quadratic equation starts with...
1) just X^2 (for ex: x^2 + 6x - 7 = 0), move constant to right, add (6/2)^2 to both sides, write left side as perfect square, and square root both sides to solve. Remember you get PLUS and MINUS solutions when you square root the constant side.
2) 2X^2 or 3X^2 or 4X^2 etc. (for ex: 2x^2 - 10x - 3 = 0), move constant to right side, DIVIDE EVERY TERM by leading coefficient 2 on left and right side, add (5/2)^2 to both sides, write left side as perfect square and square root both sides to solve.
3) -X^2 or any negative coefficient (for ex: -x^2 - 6x + 7 = 0), move constant to right side, DIVIDE EVERY TERM by -1 on left and right side. (NOTE: if you had -2x^2 in your equation, you would divide every term by -2 on left and right side). Then add (6/2)^2 to both sides, write left side as perfect square and square root both sides to solve.
If you don't have an X term in equation, (for ex: 3x^2 - 121 = 0), then you cannot complete the square. Just move the constant to the right, divide both sides by 3, and square root both sides to solve. Remember plus and minus solutions on the right.
For more of my math videos, check out: nancypi.com
I love how she admitted straight away that the only reason were learning this is because our teachers made us
If you're gonna take calculus, it is very important
Does not make it true though. It helps when looking for the roots of quadratic functions when they are irrational numbers. That is instead of using the general quadratic formula.
Try my channel mathfullyexplained
You got 333 likes I won’t ruin it
It's important because it's derives the quadratic equation.
Actually, she tells us the reason behind every step. My textbook says me to blindly do these steps and does not explain in detail. Thanks for this video!
my textbook doesn't explain steps either, so it was a lifesaver to find her video
@okar ricardo ... or why having two answers (+/-) after squaring is important
You sure it’s not because she’s hot
isnt that every god damn textbook?
Thorstein Johannessen Quadratic Equations/ expressions have 2 solutions. This is because when taking the square root of a number, for example, 25, 5 squared = 25 and -5 squared is also 25.
I like how she takes pauses to let me digest what she did and how she doesn't expect us to memorize everything. She's a good teacher. I wish she was my actual alg/trig teacher because my college professor could be a lot more helpful, especially with math but he doesn't care..
You have this in college? 😅
I am in 10th grade watching this
@@rashmit2366 8th for me
@@rashmit2366 This type of math follows you forever. I am a college grad coming back to re-learn that basics for the GRE. Never ends!
One of the greatest mysteries of mankind is - how the hell does she write backwards?
That's the question i have
the video is flipped
Jxshua Yuzn mirror board
She flipped it when she’s editing it...
I would rather believe Nancy makes magic happen in her videos.
How are all youtube teachers so much better than our own teacher?
because they love teaching, not like our teachers who prefer everything to be memorized by heart
Sawaira Azhar they’re not better xd but u wouldn’t be focusing in class as much as ur focusing in this video .. also being tired or bored in class gets u districted ..unlike being home and watching this video alone xd
ikrr
It probably has more to do with the fact that watching this video is probably the second or third time you're trying to pick up this content. Usually this is what it takes to finally start learning something. You're teacher doesn't have the ability to "hand over" the ability to do a particular topic in math, rather its not until you decide to go out of your way to really attempt to learn something that you finally will.
@@zacharyboeder7211 Thank you every math video i watch has the same comment. Its like bro your teacher has to put the concept into your head first. Thats why you are suppose to study and practice. Looking up vids is literally a form of studying. XD sadly the majority of people speak before they put any though into what they are saying
This video convinces me that everyone can learn math well if your teacher is qualified like Nancy Pi.
Simp
Try my channel mathfullyexplained
@@lightkira8396 npc
@@lightkira8396 bruh
@@mathfullyexplained but she is easier on the eyes :)
I am still fascinated by the fact she doesn't write backwards but instead writes on a window and mirrors it afterwards
Try my channel mathfullyexplained
guys stop simping for Nancy. she is very beautiful but she is a real person who can read the comments don't make her uncomfortable.
ok, thats a very good idea, but thats kind of hypocritical since you are the one simping.
but i just cant stop looking at her face instead of the numbers
SIMPPPPPPP!
Simp
@@noughsubjectivity3686 baruch hashem
i don't understand why when my professor was trying to teach this to the class, everyone including myself were very lost. You made it so much simpler. Thank you! Wish me luck on my exam guys.
Good luck:)
What happened with your exam? 😁
@@Theknowncerealkiller lol
What happened!!!
Took me like 5 mins to find this comment since I seen the replies but when I clicked on the them it didn’t direct me to my actual comment. I PASSED, in your face whoever thought i failed. Buahahhaha. You speak words into existence. 😉 say you will pass and you will !
I am failing pre calculus right now . I just wanted to let you know you saved my life
Try my channel mathfullyexplained. Many topics that can help you
I have been looking for DAYS to find an explanation on how to complete the square and this is the first one that I can fully comprehend and makes absolute sense. Thank you so much for taking the time to do this!
Thank you so much! I am in Precalc rn, and I haven't used this method in a long time but you refreshed my memory by explaining it really well!
who is watching this video the night before the test xd
W
Me 😂😂
Me
Tomorrow is my final exams and I start learning it now 🤣🤣🤣thanks Nancy 🥰
I have to do a retest
Words can't express how this was way simpler than how my teacher explained it
michaela menzel That is a common problem in math classes. Having a teaching degree in math does not mean the person can teach the subject and most math teachers cannot teach well. The ability to teach is innate in some people but few go into teaching of any kind. My math teachers were at a loss to understand why I could not grasp the material as it was so simple for them. Everything you see her writing is pure gibberish to me to this day.
Simp
My teachers showed me a mucchhhhh easier way for the first situation. You basically do what numbers multiply to make -7 which is either -1x7 or 1x-7. Then you choose between them sums and do which of those numbers add up to make 6 and you’d choose the -1x7 since -1+7=6. Soooooo simple this way. Nvm I realised this only works in some situations there’s a different method too hard for me to explain
@@SaifulIslam-uu9xz your method called crossing method
m learning a lot of things from here which i couldnt understand from my mam
Easily the best video I've found on RUclips explaining this subject. Thanks for the refresher so I can pass the tests necessary for my elementary teaching credential :)
Her smile after each step simply kills me
haha
Simp
ik like why she look like she tryna flirt with us?
Simp
down bad
Wow I just love how you teach these things so well. Your instructions are easy to follow and you make sense out if it. Thanks for your videos.
THANK YOU SOOOOO MUCH ! I've been struggling with this for over year and you taught me it in less than 20 minutes
same
Just the best video I've watched on completing the squares method of solving quadratic equations. It's all made simple. I appreciate you giving different situations, and the approach to take. Thank you.
"You don't have to like it, but you can like my video."
I did.
you and us all, chief
I had difficulties in solving a quadratic equation using completing the square method,but this video changed everything.she is a great tutor,slow but very powerful,thanks madam.
Great mathematics learning resource! Both simple to understand and comprehensive! Thanks a million nancypi!
This was really a nightmare for me, thanks for explaining the steps slowly and step by step and also explaining why things go where they go and not just assuming the viewer knows! More videos. This helped a lot!
Thank you for this video. I was having a huge issue with this method because the steps are laid out but never explained like you explained them and now it makes sense. I still don't like using this method because the quadratic formula is my favorite method oddly enough, but since I have to do it, at least it feels less intimidating now.
That was a good video Nancy. You explained that clearly, concisely and make it look 5th grade.
It is 5th grade math.
@@realdvgarg ig for indian schools....
@@anugrahahaha1908 Definitely for IB schools
@@realdvgarg ohh
thank you so much for leaving out all of the bull and getting right to the point. This was clean and easy to follow
The online lessons I do on flvs aren’t the best at teaching step by step and explaining it like this, so this video has already helped a lot for me
Thanks a lot, I have my algebra eoc 2 days from now and this was something I really struggled with. Your explanation was amazing and I can't express how happy I am especially since im in 7th grade taking algebra so you can imagine how I feel.
Quadratic formula for axis of symmetry: -b/2a
Completing square x: (b/2)^2
This is so beneficial am in grade 10 and my teacher takes 1 week to explain the whole sum nicely but here in a short period of time i get it correctly in my head.I have an exam tomorrow and this is very beneficial.Thank you NancyPi
algebra 1 is a 9th grade course??
@@wesleywilson9906 How can you assume that everyone watching this video are from US ? May be he's from a different country where Math is 'Math'; not divided by courses like Algebra1, Geometry, Algebra2 alike UK.
@@wesleywilson9906 what's in class 10th algebra just asking from a different country
maybe or he may be in a country that is simply behind lol:Like africa or the philipenes.@@HackedPC
If you notice carefully, she is teaching us how to complete the squae.
Having such a deep knowledge on why and how math works is so important, I am really learning from you
Nancy tryna teach
12 year old boys online: Loooorrrdd forgive me for what I'm boutta do
I think their is a specific website for that?...
Raul Tapia club penguin ?
Why will 12 year olds search up how to find completing the square tho??
Aren’t they a little small to do that ? ? ?
CGK Ty sure 💀
@@shobarbaba isnt algebra 1 8th and 9th grade math?
When the test is about drawing a curve, i prefer using completing the square to solve the quadratic eqn given. Bcos i can find the vector(max or min coordinate) and where it intersects the x-axis. Both just in one go.
And of course another great video!
Right, completing the square results in an equivalent equation that is
more graph user friendly.
I think it's great that Nancy tells us that there are other, maybe better, ways to solve the equation! But of course, students still have to learn this method. Personally, I like the method, but that is personal preference. Great job, Nancy!
thank you so much for showing different cases! I always watch explanation videos, but then I can't figure out how to apply them to the specific case I have in my problems because the video only shows one or two related problems. you are a life saver
Well done - concise and complete for basic purposes. Thank you!
I think the main reason that Nancy is quite successful here is that she sets out why she is taking the steps she does (as some have mentioned). As a Math(s) teacher myself, I think another reason why some of those of you who have commented here think it's easier to learn by watching a video is that, in class, the teacher is often distracted by disruptive pupils who try to make a game of stopping the learning process because they don't want to be there in class. If you've taken the trouble to look this up on the internet then you've already invested some effort yourself, and you'll take more interest in what's happening, and you won't have competing distractions either.
I was doing a one and one tutorial with a student who thought he could watch Manchester United play while I explained this to him. Yep we have multitasking students of that calibre. The father who was paying for the sessions was irate when I told him about the incident.
I watched 3 different videos before I found yours. Thank you for not skipping steps and clearly explaining why we must perform each one. Yours finally helped me!
Miss NancyPi I missed out on med school because, in high school, I didn't have a math teacher like you. I've decided to watch each one of your tutorials and conquer this beast that got in my way. Thank you
The “Matrix-like bullet-time” effect of your speech is perfect for complex subject like this.
Wish I had this 40 years ago.
Again your my go to person when I need to learn something!! I tested into college level algebra, I'm now in pre-calculus and I've never learned this. My class mates have done this in high school. Thank you again !!! This will make my Math Journey much easier. I'm 68 years young and enjoying college!!!
OK boomer
@@brighamsankar6024 Bri-sh ppl...
@@brighamsankar6024 wth..??
@@HackedPC what does that have to do with this?
@@seungmoo4131 you are too yng
I really didn't get it at first but she explains everything in such a simplified way + her way of talking is so soothing. I finally understood this topic, thank you very much, Miss Nancy!
I always love to use completing the square Nancy, but this night, I got stuck on a question, I spent nearly 2 hours going over it several times with my friends but couldn't solve it, my calculator gave me a different answer from what I was getting. This ultimately lead me to you☺️, watching your video taught me the right steps and ways I never did apply before in other CTS questions that I was able to get right. Long story short, you were ultimately helpful and now I can continue tackling all quadratic equations using completing the square method😁.
Thank you Nancy.
Great Nancy. I wish you had been my algebra teacher 50 years ago. So clear !Keep doing this work !!!
ditto.
Unc why are you watching this you’re high school days are over
You are amazing
I don't understand English good
But now I understand what do you say
Because your explain easy and you speak slowly
It's so good
Thank you
Ok Muslim
This is the most detailed and easiest to understand. Thank you so much, i cant really keep up with our class because of this and the other videos explains too fast and sometimes they say terms that aren't familiar with me, it's confusing. Thank you!
I watched 3 videos before this and none of them did it for me. This video breaks it down nicely and I feel like I have a decent understanding of it now. Thanks for the video.
Nancy It won't be long now for my nomination for my nobel prize. Something that I would like to inform you about is that I use a blue light fliter on my monitor ( called Iris) and wear glasses that block blue light to stop eye damage and preserve circadian rhythem function. So when you use the color red it is almost invisible when I watch your videos at 2 in the morning. I love your videos Thank you :)
The real question would be what kind of circadian cycle is preserving watching videos at 2am?
Shutup Sheldon Cooper
@@MajRatbag lmao bro
what amazes me the most is the way she writes on the mirror without getting confused. She writes in reverse
Try my channel mathfullyexplained
omg u explained it so well i still remember how to do this like a year later even though i havent done many questions like this
thank u so much nancy
Currently practicing for the SAT but I haven't taken a math class in like 7 years. The study guide does not give good explanations. Your videos are a lifesaver thank youuuu
Try my channel mathfullyexplained.
This just helped me out so much, thank you!
It helped me too my algebra final is tomorrow and this stuff is on it.
The fact that nacy did this even tho she knew it wasn't important just speaks to me.
Try my channel mathfullyexplained
This is one of the best tutorial because you show all the different examples. Thank you.
This is a good teacher who made us understand math lessons; therefore, anyone who abuses her won't learn math deeply!
Respect her because she is teaching her knowledge to other needy people!
Really,how I understood math from her even I didn't comprehend my school teachers as well!
Thank you Nancy, the greatest math teacher I have ever seen in my life time!
The hair flip gets me every time
holy shit u explained the whole chapter in just 3 minutes and i couldnt understand the whole week LOL! U saved my life and tomorrow is my IGCSE pray for me
how did it go
@@safin3389 wow finally someone asked about my exams 😂. It went really good now im doing A levels 😂. Looking back idk why was i struggling on this
Currently learning trig sub in Calculus 2 and having to come back to this for simplification. Thank you for making this!
thank you!!!!! I wasn't sure what number to put for the perfect square and you were the only one who said it.
If this was my math lecturer I would never miss math classes💀😂😂
Love you NancyPi 💚
Can we speak to each other through skype to learn me how to speak English?
This helped me SO MUCH! she explained every step and it was very helpful. I watched many videos but this one helped me the most! Thank you truly!
Thanks Nancy this helped me mémorise it and understand it a lot. I doubt I’ll forget how to complete the square for awhile aswell
Blink twice if you are being held hostage
The most gorgeous mathematician of all times.
OH my lord, i have never math being this detailed as good as this Thank you so much!
Try my channel mathfullyexplained
You are good with every maths concept i have ever watch u doing. Salute
Watching this 20 minutes before the test. Wish me luck.
Try my channel mathfullyexplained
@@mathfullyexplained I will sir!
Thanks ur a lot of help
Helpful and valuable! As is always the case with your videos, Nancy.
thank youu so much! i literally have been scrolling for videos nd i finally understand it now !
nobody going to talk about how she's writing backwards?
Same
Easy peasy. She recorded the video then she flipped it when she uploaded the video. Made it look like she is writing backward.
Try my channel mathfullyexplained
Why does Nancy look like she’s about to have a mental breakdown?
I dont know but it's really hot
lmao
Norcal what
Norcal 😂😂😂😂😂😂. Atleast your not lying she’s cute af
May she had the breakdown and this is the outcome
It was my first time of solving quadratic equation by completing square . Now I'm ready to go to class and solve other equations . Thank you very much☺😊
Man, in the near 20 minutes watching the video, I learned more from you than when I was in grade school and college.
"You don't have to like it (Completing the square), but you can like my video." hahah yes girl. plug.
Halfway through the video I just realised I was looking at her the whole time. I feel like a creep.
Me too
I did the same but only realized when I slowed the video down
no problem she is hot. I wish she was my teacher then I might give a damn
@@A-Jams 🤣💀
@@levirosner1728 chill bruh, he’s saying why looking at her than learning math
Love your explanation Nancy, it made this so much easier to learn. Thanks very much!
My first language isn't english but i was looking for math classes in english, bc it's easier for me to focus, then i found this channel and loved it
aw you seem so nervous it's adorable. this video was a help thanks!
I would never miss my class if i had such a beautiful maths teacher
Best math teacher in the world is Nancy
What a brilliant concept. The math teacher is a gorgeous woman so someone found a way for her to face the camera 100% of time while she's writing so we can admire her beauty and her brains simultaneously. Sheer genius.
Can you explain how to calculate Laurent series please ?
this was way more helpful than MyMathlab video. Thank you Nancy.
She's so honest i love her 😭😭
Why am I paying so much for me to look up youtube more than half the time. Thank you, this really helped me (as someone with learning disabilities as well) super thorough and no room for "but or ifs".
i like the pink numbers!
Me too
@@chandrakumar4479 question (2) answer, why we do not add the negative sin to the 5?
3:35 : perfectly balanced, as all things should be...
This helped me a lot since our teacher doesn't explain every step. I had no idea of the part where you have to square root the both sides. It just like magic how our teacher jumps from one step to another without any explanation.
This explanation is the best I saw on RUclips
the easiest method ever, South Africa Approves.
I don't even need this stuff anymore 😂😂
Maddy Holden ikr
Maddy Holden my guy I had a high A then I got a 54 on my semester test and I now have an 87
I like how she makes everything so clear ❤
Am very very grateful Madam. I've been struggling to understand these but today am enlightened with much illumination. I can now solve a complete square equation.
hi nancy pi , i am in college and there are math problems that i do not understand..can u help me?
hey Nana, beautiful the method you showed us but what about a sum like
x2+4=6X
I’m guessing the x2 is a square, legit minus 6x from both sides which gives you x^2-6x+4, (the way I do it is different but) x^2-6x+(6/2)^2-(6/2)^2+4=0 then simplify from there I cbf
Wrong hai Q3 last step X2+6x=7
Thank you. Excellent teaching skills. I was looking for a detailed explanation on this, but got stuck. Most people just do it without explaining the steps. Again, thank you.
Awesome tutoring, Teacher Nancy. Everything explained so well, step by step...Tqvm.