How do you solve $(x-4)^(3/2)= -6$ ?

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Answer 1 · 2016-04-07T15:52:22

$x=-6^(2/3)+4$

$color(blue)((x-4)^(3/2)=-6$

Take the $3/2$ root of both sides

$rarrroot(3/2)((x-4)^(3/2))=root(3/2)(-6)$

$rarrx-4=root(3/2)(-6)$

Invert the root and multiply

$rarrx-4=-6^(2/3)$

Add $4$ both sides

$rarrxcancel(-4+4)=-6^(2/3)+4$

$color(green)(rArrx=6^(2/3)+4~~7.301....$

How do you solve (x-4)^(3/2)= -6 (x-4)^(3/2)= -6 ?