Question

Question 13

Which of the following is an equivalent equation obtained by completing the square of the expression below?

x^2 + 6x - 8 = 0

Answer 1

B) (x + 3)^2 = 17

Explanation:

To complete the square you need to put x + or - half of the x coefficient.

So here it would be (x + 3)^2. However, we're trying to find x^2 + 6x - 8 = 0, not x^2 + 6x + 9 = 0, which is what (x + 3)^2 expands to. So we need to -9 from x^2 + 6x + 9 = 0 and add -8 from the original equation.

This simplifies to (x + 3)^2 - 9 - 8 = 0 --> (x + 3)^2 - 17 = 0

Then all you need to do is rearrange to give: (x + 3)^2 = 17