Posted by **Christina** on Monday, February 13, 2012 at 11:11am.

(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

- Algebra 2 -
**Reiny**, Monday, February 13, 2012 at 12:58pm
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

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