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

Apr 10, 2015

If $2 {\left(x - 2\right)}^{\frac{2}{3}} = 50$
then
${\left(x - 2\right)}^{\frac{2}{3}} = 25$

If we cube both sides we get
${\left(x - 2\right)}^{2} = {25}^{3} = {25}^{2} \cdot {5}^{2}$

or
${\left(x - 2\right)}^{2} - {125}^{2} = 0$

remember that anything of the form
$\left({a}^{2} - {b}^{2}\right)$ can be factored as $\left(a - b\right) \left(a + b\right)$

we have
$\left(\left(x - 2\right) - 125\right) \left(\left(x - 2\right) + 125\right) = 0$
or
$\left(x - 127\right) \left(x + 123\right) = 0$

so
$x = 127$
or
$x = - 123$