What does x equal if x^3-5x^2+2x=10

In order to find what x equals, we need to make it so x is on one side and what it equals, on the other.

First of all, we subtract 10 from both sides. You will now have:

x^3 - 5x^2 + 2x - 10 = 0

You will now either factor it which is recommended or use the Cubic Formula which is pretty difficult to memorize and to solve. I will now factor it.

(x - 5) (x^2 + 2) = 0

You can now take both of the expressions inside and make them equal to zero and solve them.

x - 5 = 0x = 5

x^2 + 2 = 0x^2 = - 2

x ≈ 1.41421356i

The second option is irrational and uses an imaginary number which you will start seeing in Alegbra II (or already have if you are taking it or have already passed it), so the first one which is 5, is the correct answer.

Answer: 5