# How do you solve using the completing the square method x^2+5/2x=5?

Mar 3, 2018

color(blue)(x = 1.3117, -3.8117

#### Explanation:

${x}^{2} + \left(\frac{5}{2}\right) x = 5$

Add ${\left(\frac{5}{4}\right)}^{2}$ to both sides

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

${\left(x + \left(\frac{5}{4}\right)\right)}^{2} = 5 + \left(\frac{25}{16}\right) = \frac{105}{16} = {\sqrt{\left(\frac{105}{16}\right)}}^{2}$

$\left(x + \left(\frac{5}{4}\right)\right) = \pm \sqrt{\frac{105}{16}}$

$x = \pm \left(\sqrt{\frac{105}{16}} - \left(\frac{5}{4}\right)\right)$

$x = 1.3117 , - 3.8117$