How do you solve using the completing the square method y=3x^2+24x+8?

Jun 18, 2016

$x = - 4 \pm \frac{2 \sqrt{30}}{3}$

Explanation:

$3 {x}^{2} + 24 x = - 8$.
Divide both sides by 3:
${x}^{2} + 8 x = - \frac{8}{3}$
${x}^{2} + 8 x + 16 = - \frac{8}{3} + 16 = \frac{40}{3}$
${\left(x + 4\right)}^{2} = \frac{40}{3}$
$x + 4 = \pm 2 \frac{\sqrt{10}}{\sqrt{3}} = \pm \frac{2 \sqrt{30}}{3}$
$x = - 4 \pm \frac{2 \sqrt{30}}{3}$