# How do you solve 3x^2 + 10x = 8 by completing the square?

May 12, 2016

$x = \frac{2}{3}$ or $x = - 4$

#### Explanation:

Multiply by $3$ and add $25$ to both sides to get:

$9 {x}^{2} + 30 x + 25 = 24 + 25$

which simplifies to:

${\left(3 x + 5\right)}^{2} = 49 = {7}^{2}$

So $\left(3 x + 5\right)$ is a square root of ${7}^{2}$, so it must be $7$ or $- 7$:

$3 x + 5 = \pm 7$

If $3 x + 5 = 7$, then $3 x = 2$, so $x = \frac{2}{3}$

If $3 x + 5 = - 7$, then $3 x = - 12$, so $x = - 4$