# How do you solve the quadratic equation by completing the square: 2x² - 5x - 12 = 0?

Jul 18, 2015

Solve $y = 2 {x}^{2} - 5 x - 12 = 0$

x = 5/2 +- 7/2

#### Explanation:

$2 \left({x}^{2} - \frac{5 x}{2} + \frac{25}{4}\right) = 12 + \frac{25}{2}$
(x^2 - (5x)/2 + 25/4 = 6 + 25/4 = 49/4
${\left(x - \frac{5}{2}\right)}^{2} = \frac{49}{4}$ --> $\left(x - \frac{5}{2}\right) = \pm \frac{7}{2}$

$x = \frac{5}{2} \pm \frac{7}{2}$