# How do you solve x^2 - 121 = 0?

May 21, 2018

$x = 11 \text{ }$ or $\text{ } x = - 11$

#### Explanation:

The difference of squares identity can be written:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

Note that both ${x}^{2}$ and $121 = {11}^{2}$ are perfect squares.

So we find:

$0 = {x}^{2} - 121 = {x}^{2} - {11}^{2} = \left(x - 11\right) \left(x + 11\right)$

So:

$x = \pm 11$