Question

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

In the end I got .69, but that's wrong. Please help. I don't really understand.

My work.

x-4 = -6^2/3
x=4-6^2/3
x=.6980727511

Answer 1

Your equation has no solution

If you look at the left side ....
(x-4)(3/2)
= [(x-4)^3 ] ^(1/2)
= √(x-4)^3

for all values of x < 4 , √(x-4)^3 will be undefined
for all values of x ≥0, √(x-4)^3 will be positive,
so the result can never be -6

Try this online graphing program
and in the first function line enter
(x-4)^1.5
http://rechneronline.de/function-graphs/

change the x-range from -5 to 5 TO 0 to 10
do the same for the y-range

You will see that your graph starts at (4,0) and rises continuously, no way will you ever get -6