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

Jun 5, 2017

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

Explanation:

We need to solve the equation as standard form ($a {x}^{2} + b x + c$):

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

The quadratic formula states that $\frac{- \textcolor{red}{b}}{2 \left(\textcolor{b l u e}{a}\right)} \pm \frac{\sqrt{{\textcolor{red}{b}}^{2} - 4 \times \textcolor{b l u e}{a} \times \textcolor{g r e e n}{c}}}{2 \left(\textcolor{b l u e}{a}\right)}$:

$\frac{- \left(\textcolor{red}{- 1}\right)}{2 \left(\textcolor{b l u e}{1}\right)} \pm \frac{\sqrt{{\left(\textcolor{red}{- 1}\right)}^{2} - 4 \times \textcolor{b l u e}{1} \times \textcolor{g r e e n}{1}}}{2 \left(\textcolor{b l u e}{1}\right)}$

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

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

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