# How do you solve the equation by factoring and the zero-product rule: 4x^2-25?

Dec 6, 2016

$\pm \frac{5}{2}$

#### Explanation:

Method 1

$4 {x}^{2} - 25 = 0$

factorise by difference of squares

$\left(2 x + 5\right) \left(2 x - 5\right) = 0$

solving for each bracket

$2 x + 5 = 0 \implies 2 x = - 5 \implies x = - \frac{5}{2}$

$2 x 5 = 0 \implies 2 x = 5 \implies x = \frac{5}{2}$

Method 2

rearrange the eqn for ""x

$4 {x}^{2} - 25 = 0 \implies 4 {x}^{2} = 25$

${x}^{2} = \frac{25}{4}$

$x = \pm \sqrt{\frac{25}{4}} = \pm \frac{5}{2}$