How do I solve for x in this equation?

[Cuisine123]

Homework Statement

How can I calculate x in this equation: -x^3+6x^2-11.998x+8 = 0?

Homework Equations

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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?

 

[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.

 

[tiny-tim]

Hi Cuisine123!

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

How can I calculate x in this equation: -x^3+6x^2-11.998x+8 = 0?

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! ​

 

[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.

 

[danielatha4]

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

 

[tiny-tim]

The solution of ax3+bx2+cx+d=0 is …

shouldn't there be three solutions?