# How do you solve 3t^2 – 4t = –30 by completing the square?

Jul 15, 2017

$t = \frac{2 \pm i \sqrt{86}}{3}$

#### Explanation:

Given -

$3 {t}^{2} - 4 t = - 30$

Divide all the terms by 3

$\frac{3 {t}^{2}}{3} - \frac{4 t}{3} = \frac{- 30}{3}$

${t}^{2} - \frac{4}{3} t = - 10$

divide $- \frac{4}{3}$ by 2. square it and add it on both sides

It is -4/3-:2; -4/3xx1/2=-4/6

Square the value. It is $\left(- \frac{4}{6}\right) = \frac{16}{36} = \frac{4}{9}$

Add $\frac{4}{9}$ to both sides

${t}^{2} - \frac{4}{3} t + \frac{4}{9} = - 10 + \frac{4}{9} = \frac{- 90 + 4}{9} = \frac{- 86}{9}$

${\left(t - \frac{2}{3}\right)}^{2} = - \frac{86}{9}$

$t - \frac{2}{3} = \pm \sqrt{\frac{- 86}{9}}$

$t - \frac{2}{3} = \frac{\sqrt{- 86}}{3}$

$t = \frac{2}{3} \pm \frac{i \sqrt{86}}{3}$

$t = \frac{2 \pm i \sqrt{86}}{3}$