SOLUTION: solve for x: x^3+x^2-x=3

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Question 1044584: solve for x:
x^3+x^2-x=3
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Try Rational Roots Theorem.

x%5E3%2Bx%5E2-x-3=0
Possible roots to check for are -3, -1, 1, 3; and you could expect possibly to find three roots. 


-3    |    1   1   -1   -3
      |
      |       -3   6    -15
      |___________________________
          1   -2    5   -18

-1    |    1    1    -1    -3
      |
      |        -1     0     1
      |_________________________
           1   0    -1     -2

 1    |    1    1    -1    -3
      |
      |         1    2     1
      |_____________________________
           1    2    1    -2

  3    |     1    1    -1     -3
       |
       |          3   12      33
       |_______________________________
            1     4    11     36

No rational zeros found. A real zero seems to be between x values of 1 and 3 but finding it or them requires an approximation method.

If you try a graphing tool, you will find a root or zero at close to x=1.358. This will be the ONLY real root.