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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!

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You can use the cubic formula –  Amr Nov 27 '12 at 17:14
    
Type the following into wolframaplha and you can see the exact and numeric roots: Solve[x^2(1-x) == 1, x]. Also, to do it by hand, you can follow one of the methods here: en.wikipedia.org/wiki/Cubic_function. Let us know if this helps. - A –  Amzoti Nov 27 '12 at 17:21
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There is only one real solution, there are two complex solutions. See wolframalpha.com/input/?i=solve+x%5E2%281%E2%88%92x%29%3D1 –  akkkk Nov 27 '12 at 17:22
    
Thanks. I am using this equation programatically to simulate a slinky falling. I believe the cubic formula is what I need. I'll update back here upon success : ) –  Vigrond Nov 27 '12 at 17:25

2 Answers 2

up vote 1 down vote accepted

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.

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This is because the solution of $x$ must be negative. So, when you take a square root, take the negative one. –  user1551 Dec 2 '12 at 23:11

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
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