# How do you solve x^2 − 25 = 0?

May 6, 2016

$x = \pm 5$

#### Explanation:

There are two ways of doing this.

$\textcolor{b l u e}{\text{Method 1}}$

${x}^{2} - 25 + 25 = 25$

$\text{but } - 25 + 25 = 0$

${x}^{2} = 25$

$\textcolor{b l u e}{x = \sqrt{25} = \pm 5}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Method 2}}$

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

Write$\text{ " x^2-25=0" as } {x}^{2} - {5}^{2} = 0 \to \left(x - 5\right) \left(x + 5\right) = 0$

$\textcolor{b l u e}{x = \pm 5}$