# How do I solve for x in this equation?

1. Dec 30, 2009

### Cuisine123

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

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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. Dec 30, 2009

### futurebird

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.

3. Dec 30, 2009

### tiny-tim

Hi Cuisine123!

(try using the X2 tag just above the Reply box )
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!

4. Dec 31, 2009

### HallsofIvy

By the "rational root theorem" the only possible roots are $\pm 1$, $\pm 2$, $\pm 4$, and $\pm 8$. If that "11.998" were "12", then 2 would be triple root. As it is, however, that equation has no rational roots.

5. Jan 5, 2010

### danielatha4

There is an analogous formula for polynomials of degree three: The solution of ax3+bx2+cx+d=0 is

6. Jan 5, 2010

### tiny-tim

shouldn't there be three solutions?