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Homework Help: How do I solve for x in this equation?

  1. Dec 30, 2009 #1
    1. The problem statement, all variables and given/known data
    How can I calculate x in this equation: -x^3+6x^2-11.998x+8 = 0?

    2. Relevant equations


    3. The attempt at a solution

    **I tried factoring, but how??
    **I know that the answer turns out to be x=2.16, but how did this come about?
  2. jcsd
  3. Dec 30, 2009 #2
    What course is this from? 2.6 is not an exact answer so maybe they want you to use newton's method? There are a few ways of solving this-- but the method will depend on what course you are taking.
  4. Dec 30, 2009 #3


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    Hi Cuisine123! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    It's a cubic, and you wouldn't be expected to know how to solve it in an exam.

    (Basically, you put x = y + a so that the equation is of the form y3 + Ay + B = 0, and then use a formula)

    Just use a calculator! :wink:
  5. Dec 31, 2009 #4


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    By the "rational root theorem" the only possible roots are [itex]\pm 1[/itex], [itex]\pm 2[/itex], [itex]\pm 4[/itex], and [itex]\pm 8[/itex]. If that "11.998" were "12", then 2 would be triple root. As it is, however, that equation has no rational roots.
  6. Jan 5, 2010 #5
    There is an analogous formula for polynomials of degree three: The solution of ax3+bx2+cx+d=0 is

  7. Jan 5, 2010 #6


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    shouldn't there be three solutions? :confused:
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