x^2 - 6x = 27
Take (1/2) of 6 = 3.....square this = 9.....add this to both sides
x^2 - 6x + 9 = 27 + 9 factor the left....simplify the right
(x - 3)^2 = 36 take both roots
x - 3 = ± √36
x - 3 = ± 6 add 3 to both sides
x = 3 ± 6
So
x = 3 + 6 = 9 or x = 3 - 6 = -3