Move the number term to the right side of the equation:
x^2 + 6x = -8
Complete the square:
(b/2)^2 = (6/2)^2 = 3^2 = 9
x^2+6x+9 = -8+9
(x+3)^2 = 1
Take square root in both sides of the equation:
x+3 = ± 1
Subtract 3 from both sides:
x+3-3 = 1-3
x = -2
or:
x+3-3=-1-3
x= -4