# How do you solve x^2+8x=-2 using the quadratic formula?

Apr 16, 2018

$x = - 4 \pm \sqrt{14}$

#### Explanation:

First add $2$ to each side so that the equation is in standard form: $y = a {x}^{2} + b x + c$.

${x}^{2} + 8 x + 2 = 0$

The quadratic formula is $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Here, $a$ is $1$, $b$ is $8$, and $c$ is $2$. Let's plug these numbers into the quadratic formula.

$\frac{- 8 \pm \sqrt{{8}^{2} - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$

$\frac{- 8 \pm \sqrt{64 - 8}}{2}$

$\frac{- 8 \pm \sqrt{56}}{2}$

$\frac{- 8 \pm 2 \sqrt{14}}{2}$

$- 4 \pm \sqrt{14}$

$x = - 4 \pm \sqrt{14}$

Apr 16, 2018

$x = - .258 , - 7.74$ Those are averaged btw

#### Explanation:

first move the two over to the right side
${x}^{2} + 8 x + 2 = 0$
Now plug into quadratic formula knowing that a quadratic equation is just $a {x}^{2} + b x + c = 0$ and the quadratic formula is x=(-b+-(√b^2-4ac))/(2a)
x=(-(8)+-(√(8)^2-4(1)(2)))/(2(1))
x=(-8+-(√64-8))/(2)
x=(-8+(√56))/2 or x=(-8-(√56))/2
Which means $x = - .258 , - 7.74$