# Quadratic Equation : Proof by Completing the Square

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1. Prove the Quadratic Formula by completing the square on ax^2+bx+c=0

2. A picture that is 14 in by 20 in is to have an even border. If the area of the picture and the border is 352 in^2, how wide will the border be?

https://brainmass.com/math/basic-algebra/quadratic-equation-proof-completing-square-10916

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ax2 + bx + c = 0

ax2 + bx = -c

b c

x2 + --- x = - ---

a a

b b2

---- ï‚® ----

2a 4a2

b b2 c b2

x2 + --- x + ----- = - --- + ...

#### Solution Summary

The quadratic formula is proven by completing the square. A border of a picture is calculated using a quadratic equation.

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