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....#