Question

How do you solve `a^2 - 10a +18 = 0` by completing the square?

Answer 1

`a = 5+-sqrt7`

Explanation:

Since `(a-b)^2 = a^2 - 2ab + b^2`, we need the middle term to be

`-2ab`, so we use `5` as `b`.

`a^2 - 10a + 25 = (a - 5)^2`, so `(a-5)^2 - 7 = 0 => (a-5)^2 = 7`

`a-5 = +-sqrt7 => a = 5 +- sqrt7`