Answer
$x=-2+\dfrac{\sqrt[5]{8}}{2}$
Work Step by Step
Divide 4 to both sides of the equation to obtain:
$(x+2)^5=\frac{1}{4}$
Take the fifth root of both sides:
$x+2=\sqrt[5]{\frac{1}{4}}$
Subtract 2 to both sides of the equation to obtain:
$x=-2 + \sqrt[5]{\frac{1}{4}}$
Rationalize the denominator by multiplying 8 to both the numerator and the denominator inside the radical sign to obtain:
$x = -2 +\sqrt[5]{\frac{1}{4} \cdot \frac{8}{8}}
\\x=-2 + \sqrt[5]{\frac{8}{32}}
\\x=-2+\sqrt[5]{\frac{8}{2^5}}
\\x=-2+\dfrac{\sqrt[5]{8}}{2}$
Thus, the solution to the given equation is $x=-2+\dfrac{\sqrt[5]{8}}{2}$.
