# How do you solve 36x^2 - 25 = 0?

Jun 19, 2016

$x = - \frac{5}{6} \mathmr{and} x = \frac{5}{6}$

#### Explanation:

For quadratic equations, there are 3 methods of solving them:

This equation can be factorised as the difference of two squares.

$36 {x}^{2} - 25 = 0$
$\left(6 x + 5\right) \left(6 x - 5\right) = 0$

Let each factor in turn be equal to 0.

If $6 x + 5 = 0 , \text{ or } \mathmr{if} 6 x - 5 = 0$
$6 x = - 5 \text{ } 6 x = 5$
$x = - \frac{5}{6} \text{ } x = \frac{5}{6}$

There are two solutions as we expect for a quadratic.