# How do you solve x^2 - x + 2 = 0?

Oct 10, 2015

The solutions are
color(blue)(x= (1+sqrt(-7))/2

color(blue)(x= (1-sqrt(-7))/2

#### Explanation:

${x}^{2} - x + 2$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 1 , c = 2$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(- 1\right)}^{2} - \left(4 \cdot 1 \cdot 2\right)$
$= 1 - 8 = - 7$

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 1\right) \pm \sqrt{- 7}}{2 \cdot 1} = \frac{1 \pm \sqrt{- 7}}{2}$

The solutions are
color(blue)(x= (1+sqrt(-7))/2
color(blue)(x= (1-sqrt(-7))/2