You can complete the square:
x² + 9x + 9 = x² + 9x + 81/4 - 45/4
x² + 9x + 9 = x² + 2•(9/2)x + (9/2)² - 45/4
x² + 9x + 9 = (x + 9/2)² - 45/4
Now set this equal to 0 and solve for x :
(x + 9/2)² - 45/4 = 0
(x + 9/2)² = 45/4
|x + 9/2| = 3/2 √5
x + 9/2 = 3/2 √5 or x + 9/2 = - 3/2 √5
x = -(9 - 3√5)/2 or x = -(9 + 3√5)/2
