Simple algebra question, for a program I'm writing

Question

How would I solve:

-x^3 - x - 4 = 0

You can't use quadratic, because it is to the 3rd power, right?

I know I it should come out to ~1.3788 but I'm not sure how I would derive that.

I started with:

f(x) = x + (4/(x^2 + 1)).

Solving for 0, moving the x over to the other side, multiplying by (x^2 + 1) on both sides, I end up with:

-x(x^2 + 1) = 4,

or

-x^3 - x - 4 = 0.

Answer 1

Finding roots of equations by using Newton's method or Fixed point iteration