Answer
$-1$
Work Step by Step
Subtract 8 to both sides of the equation to obtain:
$(x-1)^3=-8$
Write $-8$ as $(-2)^3$ to obtain:
$(x-1)^3=(-2)^3$
Take the cube root of both sides:
$x-1 = \sqrt[3]{(-2)^3}
\\x-1 = -2$
Add $1$ to both sides of the equation:
$x=-2+1
\\x=-1$
Thus, the solution to the given equation is $-1$.
