Answer :
To solve the quadratic equation \( x^2 + 6x + 9 = 0 \) using the Quadratic Formula, follow these steps:
1. Identify the coefficients: \( a = 1 \), \( b = 6 \), and \( c = 9 \) in the standard form \( ax^2 + bx + c = 0 \).
2. Substitute the values of \( a \), \( b \), and \( c \) into the Quadratic Formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. Plug in the values:
\[ x = \frac{-6 \pm \sqrt{6^2 - 4 \cdot 1 \cdot 9}}{2 \cdot 1} \]
4. Simplify:
\[ x = \frac{-6 \pm \sqrt{36 - 36}}{2} \]
\[ x = \frac{-6 \pm \sqrt{0}}{2} \]
5. Further simplify:
\[ x = \frac{-6 \pm 0}{2} \]
\[ x = \frac{-6}{2} = -3 \]
Therefore, the solution to the quadratic equation \( x^2 + 6x + 9 = 0 \) is \( x = -3 \).
In this case, only the answer \( x = -3 \) is correct based on the calculations.
