# How do you solve x^2 – x – 2 = 0?

Aug 1, 2015

Solve y = x^2 - x - 2 = 0

#### Explanation:

Since (a - b + c = 0), use the shortcut. The 2 real roots are:
-1 and (-c/a = 2/1 = 2)

REMINDER of Shortcut.

When (a + b + c = 0) --> 2 real roots -> 1 and (c/a)

When (a - b + c = 0) --> 2 real roots --> (- 1) and (- c/a).

Try to remember this Shortcut. It will save you a lot of time and effort!!!.

Aug 2, 2015

$x = - 1 , 2$

#### Explanation:

${x}^{2} - x - 2$ is in the form of a quadratic equation, $a x + b x + c$, where $a = 1 , b = - 1 , \mathmr{and} c = - 2$. The quadratic formula can be used to solve this problem.

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

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

$x = \frac{1 \pm \sqrt{1 + 8}}{2}$ =

$x = \frac{1 \pm \sqrt{9}}{2}$ =

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

Solve for $x$.

$x = \frac{1 + 3}{2} = \frac{4}{2} = 2$

$x = \frac{1 - 3}{2} = - \frac{2}{2} = - 1$