How to do solving equations by completing the square?

Question

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

Answer 1

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