Question

How do you solve `2(x-2)^(2/3) = 50`?

Answer 1

If `2(x-2)^(2/3) = 50`
then
`(x-2)^(2/3) = 25`

If we cube both sides we get
`(x-2)^2 = 25^3 = 25^2*5^2`

or
`(x-2)^2 - 125^2 = 0`

remember that anything of the form
`(a^2-b^2)` can be factored as `(a-b)(a+b)`

we have
`((x-2)-125)((x-2)+125) = 0`
or
`(x-127)(x+123)=0`

so
`x=127`
or
`x=-123`