Using the quadratic formula, find the solution to x^2+6x+9=0

Question

.(1 point)

Answer 1

To find the solutions to the quadratic equation $x^2+6x+9=0$ using the quadratic formula, we can 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 can plug in the values of $a$, $b$, and $c$:

1. First, we calculate the discriminant $b^2-4ac$:

$$b^2-4ac=6^2-4\cdot 1\cdot 9=36-36=0$$

2. Since the discriminant is 0, we will have exactly one real solution.

3. Now, we can substitute the values into the quadratic formula:

$$x=\frac{-6\pm \sqrt{0}}{2\cdot 1}=\frac{-6\pm 0}{2}=\frac{-6}{2}=-3$$

Thus, the solution to the equation $x^2+6x+9=0$ is

$$\boxed{{\displaystyle -3}}$$

This means there is a double root at $x=-3$.