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16 May, 06:59

X^2-14x-4=0, solve by completing the square

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  1. 16 May, 10:11
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    The answer is: x = 7 - √53 or x = 7 + √53

    The general quadratic equation is: ax² + bx + c = 0.

    But, by completing the square we turn it into: a (x + d) ² + e = 0, where:

    d = b/2a

    e = c - b²/4a

    Our quadratic equation is x² - 14x - 4 = 0, which is after rearrangement:

    So, a = 1, b = - 14, c = - 4

    Let's first calculate d and e:

    d = b/2a = - 14/2*1 = - 14/2 = - 7

    e = c - b²/4a = - 4 - (-14) ²/4*1 = - 4 - 196/4 = - 4 - 49 = - 53

    By completing the square we have:

    a (x + d) ² + e = 0

    1 (x + (-7)) ² + (-53) = 0

    (x - 7) ² - 53 = 0

    (x - 7) ² = 53

    x - 7 = + / - √53

    x = 7 + / - √53

    Therefore, the solutions are:

    x = 7 - √53

    or

    x = 7 + √53
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