The problem is a squared-2a-8=0 I do not know how to do this because I was absent. My teacher told me the answer, which is (4,-2), but I do not get how to solve it! Please help

## 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 a^{2} - 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 r^{2}. Why? This is because of the fact that a^{2} + 2ra + r^{2} = (a + r)^{2}

In your case, 2r = -2 so r = -2/2 = -1. Therefore we want the constant coefficient to be r^{2} = (-1)^{2} = 1.

a^{2} - 2a - 8 = 0

a^{2} - 2a + 1 = 9

(a - 1)^{2} = 3^{2}

a - 1 = ±3

a = 1 ± 3

a = 4 or a = -2