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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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    ax2 + bx + c = 0

    ax2 + bx = -c

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

    b b2
    ----  ----
    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.