How do you solve m^2 + m + 1 = 0  using the quadratic formula?

Jul 9, 2018

$m = \frac{- 1 + \sqrt{3} i}{2}$, $\frac{- 1 - \sqrt{3} i}{2}$

Explanation:

Solve:

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

This is a quadratic equation in standard form:

$a {x}^{2} + b x + c$,

where:

$a = 1$, $b = 1$, $c = 1$

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

Substitute $m$ for $x$. Plug in the known values.

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

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

Simplify.

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

$m = \frac{- 1 + \sqrt{3} i}{2}$, $\frac{- 1 - \sqrt{3} i}{2}$