Question

Solve this equation for x. 2/3(x+8)^2-66=0

Answer 1

Answer:

$\large\boxed{x=-8\pm3\sqrt{11}}$

Step-by-step explanation:

$\dfrac{2}{3}(x+8)^2-66=0\qquad\text{add 66 to both isdes}\\\\\dfrac{2}{3}(x+8)^2-66+66=0+66\\\\\dfrac{2}{3}(x+8)^2=66\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}(x+8)^2=(3)(66)\\\\2(x+8)^2=198\qquad\text{divide both sides by 2}\\\\\dfrac{2\!\!\!\!\diagup^1(x+8)^2}{2\!\!\!\!\diagup_1}=\dfrac{198\!\!\!\!\!\diagup^{99}}{2\!\!\!\!\diagup_1}\\\\(x+8)^2=99\iff x+8=\pm\sqrt{99}\qquad\text{subtract 8 from both sides}$

$x+8-8=-8\pm\sqrt{(9)(11)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=-8\pm\sqrt9\cdot\sqrt{11}\\\\x=-8\pm3\sqrt{11}$