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

Aug 6, 2015

Use the quadratic formula to get
$\textcolor{w h i t e}{\text{XXXX}}$$x = 1 \pm \sqrt{3}$

#### Explanation:

For any quadratic equation of the form
$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x + c = 0$
the solutions are given by the formula
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Given ${x}^{2} - 2 x - 2 = 0$
$a = 1$$\textcolor{w h i t e}{\text{XXXX}}$$b = - 2$$\textcolor{w h i t e}{\text{XXXX}}$$c = - 2$
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{2 \pm \sqrt{{\left(- 2\right)}^{2} - 4 \left(1\right) \left(- 2\right)}}{2 \left(1\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{2 \pm \sqrt{12}}{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{2 \pm 2 \sqrt{3}}{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 1 \pm \sqrt{3}$