How do you solve for x in $3 {(x - 6)}^{\frac{5}{2}} = 96$ $3(x-6)^(5/2) = 96$ ?

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Answer 1 · 2015-04-24T00:08:06

$3 {(x - 6)}^{\frac{5}{2}} = 96$ $3(x-6)^(5/2)=96$

Reduce by removing obvious common factor ( $3$ $3$ )
$\to {(x - 6)}^{\frac{5}{2}} = 32$ $rarr (x-6)^(5/2)=32$

Note that $32 = 2^{5}$ $32 =2^5$ so we can take the 5th root of both sides
$\to {(x - 6)}^{\frac{1}{2}} = 2$ $rarr (x-6)^(1/2) = 2$

Square both sides to clear the root on the left side
$\to x - 6 = 4$ $rarr x-6 = 4$

Isolate $x$ $x$
$\to x = 10$ $rarr x=10$

How do you solve for x in 3(x-6)^(5/2) = 963(x−6)52=963(x-6)^(5/2) = 96?