Quadratic equation with exponents

[Nico Nico Niii]

Hi there. This problem might be easy but i have some difficulty in how cancelation works in this problem because there are 2 x given. (x^(2)-3x-4)^(3)=x^(3). After I took the cube root of both sides, I tried to eliminate x on the right by canceling it with the -3x. Thus my answer becomes x^(2)-7 and my final answer was √7. Yet it does not satisfy the given equation. I've tried different methods such as factoring yet it still doesn't work. May I ask for a little assistance just even after i took the cube root of it. Thanks

 

[mmm4444bot]

… i have some difficulty in how [cancellation] works in this problem because there are 2 x given.

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

After I took the cube root of both sides, I tried to eliminate x on the right by canceling it with the -3x.

"Cancel" is the wrong terminology, here. You're talking about "Combining Like-Terms".

In other words, after you took the cube root of each side, you had:

x^2 - 3x - 4 = x

The next step is to subtract x from each side, and then "combine like-terms" on each side, to simplify.

Thus my answer becomes x^(2) - 7

"Answer" is not the right word, here. You're talking about an intermediate "result".

You have not properly combined like-terms, on the left-hand side of the equation. Maybe you confused 3x with 3?

Also, the right-hand of your resulting equation is missing, so I cannot tell what you got on the right.

Try subtracting x from each side, again. Write out this step completely, and then carefully simplify each side, by combining like-terms:

x^2 - 3x - 4 - x = x - x

PS: None of the grouping symbols highlighted in red are needed.