Answer
Algebraically, we get $x=-2+\frac{2}{3}\sqrt[5]{81}$.
Graphically, we get $x=-0.3945$.
Work Step by Step
Solve algebraically:
$6(x+2)^5=64$ (Divide by 6)
$(x+2)^5=\frac{32}{3}$
$(x+2)^5=\frac{2^5\cdot 81}{3^5}$ (Take the fifth root)
$x+2=\frac{2}{3}\sqrt[5]{81}$
$x=-2+\frac{2}{3}\sqrt[5]{81}$
Solve graphically:
We sketch the graphs of $y_1=6(x+2)^5$ and $y_2=64$ as shown below.
Both intersect at $x=-0.3945$.
So, the solution is $x=-0.3945$.
