Question

Using the quadratic formula, find the solution to x2+6x+9=0 .(1 point)

Answer 1

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 \(x = -3\).