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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?

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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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ax2 + bx + c = 0

ax2 + bx = -c

b c
x2 + --- x = - ---
a a

b b2
----  ----
2a 4a2

b b2 c b2
x2 + --- x + ----- = - --- + ...

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