Question

8.0x=x^3+3.0x^2 solve for x

Answer 1

First of all, move all terms to the same side:

`x^3 + 3x^2 - 8 x = 0`

You can factor an x, which means that
`x = 0` is a solution:

`x(x^2+3x-8)`

This expression is further factorizable if the quadratic equation has any solution. Using the quadratic formula, we can find that they are

`x_(1,2) = -(3 \pm √(41))/(2)`

So, we have

`x(x^2+3x+8) = 0 = \iff x = 0,\quad x =-(3 + √(41))/(2) ,\quad x =-(3 - √(41))/(2)`