What is the answer to (x-2)^{5/2}=32 ?

The answer to (x-2)^{5/2}=32 is x=6

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(x-2)^{5/2}=32

(x - 2)^{\frac{5}{2}} = 32

x = 6

Solution steps

(x - 2)^{\frac{5}{2}} = 32

Take both sides of the equation to the power of

\frac{2}{5} : (x - 2) = 4

(x - 2) = 4

Solve

(x - 2) = 4 : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

x^{- \frac{1}{2}} = 4

(x - 6) = x - 6 + 12

x + 4 = 2 - 2 x

x + 13 = x + 1

2 = x^{2} + x - 2