Question 442565
{{{cartoon(
(x-1)^3/2 =27,(x-1)^3/highlight(2) = 27, (x-1)^3 = 54, (x-1)^highlight(3)=54, x-1 = root(3,54),x-1 = root(3,2) * root(3,3^3), x-1 = 3*root(3,2),x = 3*root(3,2)+1, highlight(x=3*root(3,2)+1))}}}

Multiply both sides by 2.
Take the cube root of both sides.
Simplify {{{root(3,54) = 3*root(3,2)}}}
Add 1 to both sides.