$1 x^{2}+6 x+9=0$

Step 1 ：Given the quadratic equation: \(x^2 + 6x + 9 = 0\)

Step 2 ：Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 3 ：Substitute the coefficients: a = 1, b = 6, and c = 9

Step 4 ：Calculate the discriminant: \(\Delta = b^2 - 4ac = 6^2 - 4(1)(9) = 0\)

Step 5 ：Since the discriminant is 0, there is only one solution for x.

Step 6 ：Find the solution: \(x = \frac{-6 \pm \sqrt{0}}{2(1)} = -3\)

Step 7 ：\(\boxed{x = -3}\)