# Question #dd07c

Apr 22, 2016

$x = 2 , - 1$

#### Explanation:

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

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

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

Add the square of -1/2 (the coefficient of the $- x$ divided by 2) to both sides. Remember, the standard form is ${x}^{2} + 2 a x + {a}^{2}$
${x}^{2} - x + \frac{1}{4} = 2 + \frac{1}{4}$

Factor the left side of the equation
$\left(x - \frac{1}{2}\right) \left(x - \frac{1}{2}\right) = 2 \frac{1}{4}$
${\left(x - \frac{1}{2}\right)}^{2} = 2 \frac{1}{4}$

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

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

$x = \frac{1}{2} \pm 1 \frac{1}{2} = 2 , - 1$