Answer
$x$ $\approx$ $-0.39$
Work Step by Step
Given equation is-
$6(x+2)^{5}$ = $64$
Algebraic Solution:
$6(x+2)^{5}$ = $64$
i.e. $(x+2)^{5}$ = $\frac{64}{6}$ = $\frac{32}{3}$
i.e. $(x+2)$ =$\sqrt[5] {\frac{32}{3}} $
i.e. $(x+2)$ =$\sqrt[5] {\frac{2^{5}}{3}} $
i.e. $(x+2)$ =$2\sqrt[5] {\frac{1}{3}} $
i.e. $x$ =$2\sqrt[5] {\frac{1}{3}} -2 $
i.e. $x$ =$2(\sqrt[5] {\frac{1}{3}} -1) $
Using calculator-
$x$ = $-0.39452$
$x$ $\approx$ $-0.39$
Graphical Solution:
$6(x+2)^{5}-64$ = $0$
Now graphing $y$ = $6(x+2)^{5}-64$
We get $x-intercepts $ as $-0.39452$
i.e. $x$ $\approx$ $-0.39$
