# How do you solve 2z^2 - 10z = -12?

Jul 26, 2016

2 and 3

#### Explanation:

$y = 2 {z}^{2} - 10 z + 12 = 0$
Use the improved quadratic formula in graphic form (Socratic Search)
$D = {d}^{2} = {b}^{2} - 4 a c = 100 - 96 = 4$ --> $d = \pm 2$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{10}{4} \pm \frac{2}{4}$
$x = \frac{5}{2} \pm \frac{1}{2} = \frac{5 \pm 1}{2} =$
$x 1 = \frac{6}{2} = 3$ and $x 2 = \frac{4}{2} = 2$