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Math Help - Complete the square

  1. #1
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    Complete the square

    Complete the square on:

    x^2 - 8k



    and


    k^2 + 4k
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  2. #2
    Moo
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    Hello,

    Isn't it k^2 - 8k in the first one ?


    You must associate these expressions with the formulas you should know :

    (a-b) = a - 2ab + b

    (a+b) = a + 2ab + b

    So in each case, you'll got to find what is a. Then find 2ab. Hence, you got b, and you complete your expressions with b
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    Quote Originally Posted by stellina_91 View Post
    Complete the square on:

    x^2 - 8k
    Let's demonstrate with the first one:
    k^2 - 8k

    We are comparing this to
    k^2 + 2bk + b^2 = (k + b)^2

    So by matching the coefficients of the linear (k) term we see that
    2b = -8 \implies b = -4

    Thus we need to add b^2 = (-4^2) = 16 to the expression. But we can't do that and not change the expression. So we have to be a bit clever about this and add 16 - 16 = 0 to the expression. That way the value of the expression does not change.

    So
    k^2 - 8k = k^2 - 8k + 16 - 16 = (k - 4)^2 - 16

    You do the second one.

    -Dan
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