Answer
Thus, the solutions to the given equation are $-5$ and $1$.
Work Step by Step
Add 81 to both sides of the equation to obtain:
$(x+2)^4=81$
Write $81$ as $3^4$ to obtain:
$(x+2)^4=3^4$
Take the fourth root of both sides:
$x+2 = \pm \sqrt[4]{3^4}
\\x+2 = \pm3$
Subtract $2$ to both sides of the equation:
$x=\pm3 - 2
\\x=-2 \pm 3$
The solutions are:
$x_1=-2+3 = 1
\\x_2=-2-3=-5$
Thus, the solutions to the given equation are $-5$ and $1$.
