## College Algebra 7th Edition

$x=-2+\dfrac{\sqrt[5]{8}}{2}$
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 $x=-2+\dfrac{\sqrt[5]{8}}{2}$.