# How do you solve x(x+6)=-2 using the quadratic formula?

Oct 31, 2017

When given an equation of the form, $a {x}^{2} + b x + c = 0$, one can find the value(s) of x by substituting the values for a, b, and c into the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 \left(a\right) \left(c\right)}}{2 a}$

#### Explanation:

The given equation $x \left(x + 6\right) = - 2$ is not in the form specified in the answer, therefore, we must put it in that form.

Use the distributive property on the left side:

${x}^{2} + 6 x = - 2$

Add 2 to both sides:

${x}^{2} + 6 x + 2 = 0$

By observation, $a = 1 , b = 6 , \mathmr{and} c = 2$

Substitute these values into the quadratic formula:

$x = \frac{- 6 \pm \sqrt{{6}^{2} - 4 \left(1\right) \left(2\right)}}{2 \left(1\right)}$

$x = \frac{- 6 \pm \sqrt{36 - 8}}{2}$

$x = \frac{- 6 \pm \sqrt{28}}{2}$

$x = \frac{- 6 \pm 2 \sqrt{7}}{2}$

$x = - 3 \pm \sqrt{7}$

$x = - 3 - \sqrt{7}$ and $x = - 3 + \sqrt{7}$