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Quadratic formula proof review

A text-based proof (not video) of the quadratic formula
The quadratic formula says that
x=b±b24ac2a
for any quadratic equation like:
ax2+bx+c=0
If you've never seen this formula proven before, you might like to watch a video proof, but if you're just reviewing or prefer a text-based proof, here it is:

The proof

We'll start with the general form of the equation and do a whole bunch of algebra to solve for x. At the heart of the proof is the technique called completing the square. If you're unfamiliar with this technique, you may want to brush up by watching a video.

Part 1: Completing the square

ax2+bx+c=0(1)ax2+bx=c(2)x2+bax=ca(3)x2+bax+b24a2=b24a2ca(4)(x+b2a)2=b24a2ca(5)

Part 2: Algebra! Algebra! Algebra!

Remember, our goal is to solve for x.
(x+b2a)2=b24a2ca(5)(x+b2a)2=b24a24ac4a2(6)(x+b2a)2=b24ac4a2(7)x+b2a=±b24ac4a2(8)x+b2a=±b24ac2a(9)x=b2a±b24ac2a(10)x=b±b24ac2a(11)
And we're done!

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