Question

How do you solve the equation $\frac{2}{3}{(x+8)}^2-66=0$?

Answer 1

$x=-8\pm 3\sqrt{11}$
Explanation:
$\frac{2}{3}(x+8{)}^2-66=0$
$\frac{2}{3}(x+8{)}^2=66\to$ add $66$ to both sides
$\frac{3}{2}\times \frac{2}{3}(x+8{)}^2=66\times \frac{3}{2}\to$ multiply both sides by $\frac{3}{2}$
$(x+8{)}^2=99$
$x+8=\pm \sqrt{99}\to$ 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