Question

Use completing the square to solve for x in the equation (x minus 12) (x + 4) = 9.
x = –1 or 15
x = 1 or 7
x = 4 plus-or-minus StartRoot 41 EndRoot
x = 4 plus-or-minus StartRoot 73 EndRoot

Answer 1

Start by expanding and moving 9 to the left:
(x − 12)(x + 4) = 9
x^2 − 8x − 48 = 9
x^2 − 8x − 57 = 0

Complete the square on x^2 − 8x:
x^2 − 8x = (x − 4)^2 − 16

So
(x − 4)^2 − 16 − 57 = 0
(x − 4)^2 − 73 = 0
(x − 4)^2 = 73

Thus x − 4 = ±√73, so
x = 4 ± √73.

(Option: x = 4 ± √73)