# How do you complete the square to solve 2x^2 - 10x - 20 = 8?

May 23, 2015

First notice that all the terms are divisible by $2$, so let us divide both sides of the equation by $2$ to get:

$4 = {x}^{2} - 5 x - 10$

$= {x}^{2} - 5 x + \frac{25}{4} - \frac{25}{4} - 10$

$= {\left(x - \frac{5}{2}\right)}^{2} - \frac{25}{4} - \frac{40}{4}$

$= {\left(x - \frac{5}{2}\right)}^{2} - \frac{65}{4}$

Add $\frac{65}{4}$ to both ends to get:

${\left(x - \frac{5}{2}\right)}^{2} = 4 + \frac{65}{4} = \frac{16}{4} + \frac{65}{4} = \frac{81}{4} = {\left(\frac{9}{2}\right)}^{2}$

So

$\left(x - \frac{5}{2}\right) = \pm \frac{9}{2}$

Add $\frac{5}{2}$ to both sides to get:

$x = \frac{5}{2} \pm \frac{9}{2}$

That is $x = - \frac{4}{2} = - 2$ or $x = \frac{14}{2} = 7$.