Solve $x^2(1-x) = 1$

Question

I have a problem $x^2(1-x) = 1$

This can be simplified ( I think ) to $-x^3 + x^2 - 1 = 0$

Google shows that there is 1 solution for this in its graph.

I am not sure how to get to that solution though? I need to get $x$ on one side of the equation. It doesn't seem to fit the quadratic format, but I may be wrong.

Help me remember my algebra :p

Thanks!

Answer 1

If you are only interested in the numerical value of the real solution, the iteration $x\leftarrow-1/\sqrt{1-x}$ with initial value $x=0$ will also give you the solution $x=-0.75487766624669$ to 14 decimal places after 23 iterations.

Answer 2

Answer was in the comments. I used the Cubic Formula to solve.

Additionally, I was using Octave to do simulations that utilize this equation.

Octave actually has a roots function to find the roots of a given polynomial

example:

octave:1> c = [1,1,0,-1]
c =

   1   1   0  -1

octave:2> roots(c)
ans =

  -0.87744 + 0.74486i
  -0.87744 - 0.74486i
   0.75488 + 0.00000i