x^2 + 8x + 9 = 32
There's an 8 on the x in the middle. Half of 8 is 4. 4 squared is 16.
x^2 + 8x + 16 - 16 + 9 = 32
x^2 + 8x + 16 - 7 = 32
x^2 + 8x + 16 = 39
(x + 4)^2 = 39
x + 4 = +- sqrt(39)
x = +- sqrt(39) - 4
x = -sqrt(39) - 4 or x = sqrt(39) - 4