How to Solve By Completing the Square (NancyPi)

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.

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.

[dylanmcconnell]

I love how she admitted straight away that the only reason were learning this is because our teachers made us

[isaacsamuel]

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!

[sawairaazhar]

How are all youtube teachers so much better than our own teacher?

[alexiswaller]

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..

[susiemurray]

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.

[seansasaki]

This video convinces me that everyone can learn math well if your teacher is qualified like Nancy Pi.

[electricdreamer]

One of the greatest mysteries of mankind is - how the hell does she write backwards?

[Nat]

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.

[GongsBrandCube]

I am still fascinated by the fact she doesn't write backwards but instead writes on a window and mirrors it afterwards

[jennaschulman]

I am failing pre calculus right now . I just wanted to let you know you saved my life

[IceCreamMilkshake]

Words can't express how this was way simpler than how my teacher explained it

[views-dzcg]

Nancy tryna teach

12 year old boys online: Loooorrrdd forgive me for what I'm boutta do

[enyafredericks]

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!

[kanankanan]

Her smile after each step simply kills me

[laneyb]

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

[rickeyestes]

That was a good video Nancy. You explained that clearly, concisely and make it look 5th grade.

[Nishaaat]

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

[daithi]

"You don't have to like it, but you can like my video."
I did.

[alissamerz]

Easily the best video I've found on YouTube explaining this subject. Thanks for the refresher so I can pass the tests necessary for my elementary teaching credential :)

[rayg.]

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! <3