Question

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

Answer 1

`\large\boxed{x=-8\pm3√(11)}`

Explanation:

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

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