# How do you solve  x^2=-5x-5?

Aug 1, 2015

$\textcolor{red}{x = \frac{\sqrt{5} - 5}{2}}$ and $\textcolor{red}{x = - \frac{\sqrt{5} + 5}{2}}$

#### Explanation:

${x}^{2} = - 5 x - 5$

Convert the equation to standard form,

$a {x}^{2} + b x + c = 0$

${x}^{2} + 5 x + 5 = 0$

$a = 1$, $b = 5$, and $c = 5$

x = (-b±sqrt(b^2 -4ac))/(2a) = (-5±sqrt(5^2-4×1×5))/(2×1) = (-5±sqrt(25-20))/2 = (-5±sqrt5)/2
$x = \frac{- 5 + \sqrt{5}}{2}$ and $x = \frac{- 5 - \sqrt{5}}{2}$
$x = \frac{\sqrt{5} - 5}{2}$ and $x = - \frac{\sqrt{5} + 5}{2}$