To solve the quadratic equation \( x^2 + 6x + 9 = 0 \) using the quadratic formula, we first identify the coefficients:
- \( a = 1 \)
- \( b = 6 \)
- \( c = 9 \)
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Now, we will calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot 9 = 36 - 36 = 0 \]
Since the discriminant is zero, there is one real solution (a repeated root). Now we can substitute \( a \), \( b \), and the discriminant into the quadratic formula:
\[ x = \frac{-6 \pm \sqrt{0}}{2 \cdot 1} \]
This simplifies to:
\[ x = \frac{-6}{2} = -3 \]
Thus, the solution to the equation \( x^2 + 6x + 9 = 0 \) is:
\[ \boxed{-3} \]