# How do you solve the equation 2/3(x+8)^2-66=0?

Jul 18, 2017

$x = - 8 \pm 3 \sqrt{11}$

#### Explanation:

$\frac{2}{3} {\left(x + 8\right)}^{2} - 66 = 0$

$\frac{2}{3} {\left(x + 8\right)}^{2} = 66$ $\to$add $66$ to both sides

$\textcolor{b l u e}{\frac{3}{2}} \cdot \frac{2}{3} {\left(x + 8\right)}^{2} = 66 \cdot \textcolor{b l u e}{\frac{3}{2}}$ $\to$multiply both sides by $\frac{3}{2}$

${\left(x + 8\right)}^{2} = 99$

$x + 8 = \pm \sqrt{99}$ $\to$take the square root of both sides

$x + 8 = \pm 3 \sqrt{11}$ $\to$simplify the radical

$x = - 8 \pm 3 \sqrt{11}$ $\to$subtract $8$ from both sides

Jul 18, 2017

color(magenta)(x=-8+3sqrt11 or x=-8-3sqrt11

#### Explanation:

$\frac{2}{3} {\left(x + 8\right)}^{2} - 66 = 0$

$\therefore \frac{2}{3} \left({x}^{2} + 16 x + 64\right) - 66 = 0$

$\therefore \frac{2}{3} {x}^{2} + \frac{32}{3} x + \frac{128}{3} - 66 = 0$

$\therefore \frac{2}{3} {x}^{2} + \frac{32}{3} x + \frac{128}{3} - \frac{198}{3} = 0$

$\therefore \frac{2}{3} {x}^{2} + \frac{32}{3} x - \frac{70}{3} = 0$

multiply both sides by 3

$\therefore 2 {x}^{2} + 32 x - 70 = 0$

$\therefore 2 \left({x}^{2} + 16 x - 35\right) = 0$

$\therefore {x}^{2} + 16 x - 35 = 0$

$\therefore x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 1 , b = 16 , c = - 35$

$\therefore x = \frac{- 16 \pm \sqrt{{16}^{2} - 4 \left(1\right) \left(- 35\right)}}{\left(2\right) \left(1\right)}$

$\therefore x = \frac{- 16 \pm \sqrt{256 + 140}}{2}$

$\therefore x = \frac{- 16 \pm \sqrt{396}}{2}$

$x = \frac{- 16 \pm \sqrt{11 \cdot 3 \cdot 3 \cdot 2 \cdot 2}}{2}$

$\therefore x = \frac{- 16 \pm 6 \sqrt{11}}{2}$

$\therefore {\cancel{- 16}}^{\textcolor{m a \ge n t a}{- 8}} / {\cancel{2}}^{\textcolor{m a \ge n t a}{1}} \pm \frac{{\cancel{- 6}}^{\textcolor{m a \ge n t a}{- 3}} \sqrt{11}}{\cancel{2}} ^ \textcolor{m a \ge n t a}{1}$

$\therefore - 8 \pm 3 \sqrt{11}$

:.color(magenta)(x=-8+3sqrt11,x=-8-3sqrt11