# How do you solve x^2+2x-120=0 by completing the square?

Oct 11, 2016

$x = 10$ or $x = - 12$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Use this with $a = \left(x + 1\right)$ and $b = 11$ as follows:

$0 = {x}^{2} + 2 x - 120$

$\textcolor{w h i t e}{0} = {x}^{2} + 2 x + 1 - 121$

$\textcolor{w h i t e}{0} = {\left(x + 1\right)}^{2} - {11}^{2}$

$\textcolor{w h i t e}{0} = \left(\left(x + 1\right) - 11\right) \left(\left(x + 1\right) + 11\right)$

$\textcolor{w h i t e}{0} = \left(x - 10\right) \left(x + 12\right)$

Hence roots $x = 10$ and $x = - 12$