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