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How to do solving equations by completing the square?

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1 Answer

In any quadratic, before you complete the square, you first divide through by the leading coefficient to make it 1. In your case of a2 - 2a - 8 = 0, the leading coefficient is already 1.

Now you can complete the square. If the linear coefficient is 2r then you want to make the constant coefficient r2. Why? This is because of the fact that a2 + 2ra + r2 = (a + r)2
 In your case, 2r = -2 so r = -2/2 = -1. Therefore we want the constant coefficient to be r2 = (-1)2 = 1.

a2 - 2a - 8 = 0

a2 - 2a + 1 = 9

(a - 1)2 = 32

a - 1 = ±3

a = 1 ± 3

a = 4 or a = -2