Asked by Courtney

Directions: Find the REAL solutions of the equation

x^3-2.6x^2=3.93


Please help, its for my final!
Answered by Reiny
I don't like decimals ,so multiply each term by 100

100x^3 - 260x^2 = 393
100x^3 - 260x^2 - 393 = 0

I don't know what level of math this is, but there is no simple algebraic way to solve this cubic.
I tried the usual
f(1), f(-1), f(3), etc to find a zero but nothing there.

I finally tried my trusty on line cubic equation solver
http://www.1728.com/cubic.htm
and found one real root, with 2 complex roots tossed in.

Have you been given some cubic equation formula?
This would be a very unlikely equation for a final.
Answered by Courtney
No. I swear its on my final for college algebra.

I know the answer is 3.028
Answered by Reiny
Are you familiar with Newton's Method perhaps?

x<sub>new</sub> = x<sub>old</sub> - f(<sub>old</sub>)/ f ' (<sub>old</sub>)

let f(x) = 100x^3 - 260x^2 - 393
f '(x) = 300x^2 - 520x

guess at old = 3 (the graph showed an x -intercept at around 3)

old --- new
3 ....... 3.02895
3.02895 3.02849
3.02849 3.02849 same answer to 5 decimals

no matter what you pick as your first "old" it will eventually close in on that answer, it will just take more steps.
The closer your first guess, the faster the process.
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