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

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 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:

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