# How do you solve (x- 5/2) ^2 = 9/4?

Jun 27, 2016

$x = 4 \mathmr{and} x = 1$

#### Explanation:

Find the square root of both sides, remembering that there can be a positive or negative root.

${\left(x - \frac{5}{2}\right)}^{2} = \frac{9}{4}$

$\sqrt{{\left(x - \frac{5}{2}\right)}^{2}} = \pm \sqrt{\frac{9}{4}}$

$x - \frac{5}{2} = \frac{3}{2} \text{ or } x - \frac{5}{2} = - \frac{3}{2}$

$x = \frac{3}{2} + \frac{5}{2} \text{ or } x = - \frac{3}{2} + \frac{5}{2}$

$x = \frac{8}{2} \text{ or } x = \frac{2}{2}$

$x = 4 \mathmr{and} x = 1$