# How do you solve x^2-x= -1 using the quadratic formula?

Jul 26, 2016

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

#### Explanation:

The quadratic formula for a general quadratic equation $a {x}^{2} + b x + c = 0$ is given by:

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

For the equation:

${x}^{2} - x = - 1$

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

you get

a=1; b=-1 and c = 1

by substituting these values in the quadratic formula:

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

$x = \frac{1 \pm \sqrt{1 - 4}}{2}$

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

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