# How do you solve using the completing the square method 2x^2+7x-5=0?

Mar 3, 2018

color(blue)(x = (1/4) (3sqrt11 - 7), -(1/4)(3sqrt11 + 7)

#### Explanation:

$2 x 2 + 7 x - 5 = 0$

Dividing by 2, $x 2 + 2 \cdot \left(\frac{7}{4}\right) x = \frac{5}{2}$

Adding ${\left(\frac{7}{4}\right)}^{2}$ to both sides,

x^2 = (2*(7/4)x + (7/4)^2 = 5/2 + (7/4)^2 = 99/16

${\left(x + \frac{7}{4}\right)}^{2} = {\left(\sqrt{\frac{99}{16}}\right)}^{2}$

$x + \frac{7}{4} = \pm \sqrt{\frac{99}{16}}$

$x = \sqrt{\frac{99}{16}} - \frac{7}{4} , - \sqrt{\frac{99}{16}} - \frac{7}{4}$

$x = \left(\frac{1}{4}\right) \left(3 \sqrt{11} - 7\right) , - \left(\frac{1}{4}\right) \left(3 \sqrt{11} + 7\right)$