Question

How do you solve `x^3 + 4x^2 - x=0`?

Answer 1

I found three solutions as follows:
`x_1=0`
`x_2=-2+sqrt(5)`
`x_3=-2-sqrt(5)`

Explanation:

You can start collecting `x` to get:
`x(x^2+4x-1)=0`
So you get:
`x_1=0`
`x^2+4x-1=0` that can be solved using the Quadratic Formula as:
`x_(2,3)=(-4+-sqrt(16+4))/2` which gives you two additional solutions:
`x_2=(-4+sqrt(20))/2=-2+sqrt(5)`
and:
`x_3=(-4-sqrt(20))/2=-2-sqrt(5)`

Where I used the fact that `sqrt(20)=sqrt(5*4)=2sqrt(5)`