# How do you solve the quadratic x^2+x=-1 using any method?

Aug 14, 2016

Use the quadratic formula to find roots:

$- \frac{1}{2} \pm \frac{\sqrt{3}}{2} i$

#### Explanation:

If you add $1$ to both sides, the equation becomes:

${x}^{2} + x + 1 = 0$

This is in the form $a {x}^{2} + b x + c = 0$ with $a = b = c = 1$.

This has roots given by the quadratic formula:

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

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

$= \frac{- 1 \pm \sqrt{- 3}}{2}$

$= - \frac{1}{2} \pm \frac{\sqrt{3}}{2} i$