# How do you solve x^2=-x+7 using the quadratic formula?

Feb 25, 2016

The roots are $2.192582404$ and $- 3.192582404$

#### Explanation:

Re-arrange the equation into a standard form
$a {x}^{2} + b x + c = 0$

in this case, that would be

1) ${x}^{2} + x - 7 = 0$

Using the quadratic formula $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substituting the values from equation into the general formula

$\frac{- 1 \pm \sqrt{{1}^{2} - 4 \cdot 1 \cdot - 7}}{2 \cdot 1}$

simplifies to
$\frac{- 1 \pm \sqrt{29}}{2}$

or $2.192582404$ and $- 3.192582404$