# How do you solve x^2=121?

##### 1 Answer
Mar 10, 2018

$x 1 = - 11 ,$ $x 2 = 11$

#### Explanation:

Move the constant to the left and change its sign

${x}^{2} - 121 = 0$

Using ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$, Factor the expression

$\left(x - 11\right) \left(x + 11\right) = 0$

When the product of factors equals 0, at least one factor is 0

$x - 11 = 0$

$x + 11 = 0$

Solve both equations for $x$

$x = 11$

$x = - 11$

The final solutions are

∴ $x 1 = - 11 ,$ $x 2 = 11$