To solve the quadratic equation \(x^2 + 6x + 9 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\):
- \(a = 1\)
- \(b = 6\)
- \(c = 9\)
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 0, there is one repeated root. Now, we can use the quadratic formula to find the solution:
\[ x = \frac{{-6 \pm \sqrt{0}}}{2 \cdot 1} = \frac{{-6}}{2} = -3 \]
Thus, the solution to the equation \(x^2 + 6x + 9 = 0\) is:
\[ x = -3 \]
This means the equation has one double root at \(x = -3\).
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