Posted by **Kari** on Thursday, November 24, 2011 at 3:49pm.

Hi this is a dimensional analysis problem,I want to solve for x.

300x^2 -16.667x^3+(-7200)=0

after getting

300x^2 -16.667x^3=7200

I really don't know what to do.

Plz help.

Math (Dimensional Analysis) - Reiny, Thursday, November 24, 2011 at 11:27am

This is very effective online webpage.

I simply entered the equation in the form

300x^2 -16.667x^3-7200 = 0

It gave my 3 real answers and the corresponding gram of

f(x) = 300x^2 -16.667x^3-7200

Hi, I know I already posted this, i already used Wolfram Alpha before, but in this case they don't show the step by step solution, so I know the answers but I don't know how to get them. I'll appreciate it if I can be told how to solve this problem.

- Math -
**Reiny**, Thursday, November 24, 2011 at 7:22pm
Ok Kari, let's have a closer look at your equation.

the 16.667 appears to be a rounding of 16.6666....

or 16 2/3 which would be 50/3

so your equation is

300x^2 - (50/3)x^2 - 7200 = 0

times 2

900x^2 - 50x^3 - 21600 = 0

divide by 50

18x^2 - x^3 - 432 = 0

I now cheated and used Wolfram again and found an exact answer of x = 6

( Or we could have used x = ±1, ±2, ±3, ±4, ±6, etc, that is, factors of 432, and eventually we could find that x=6 works)

so x-6 is a factor, and by synthetic division,

18x^2 - x^3 - 432 = (x-6)(-x^2 + 12x + 72)

so using the quadratic formula on

x^2 - 12x - 72 - 0

x = (12 ± √432)/2 = (12 ± 12√3)/2

= 6 ± 6√3

when I answered before I took the equation exactly as you typed it.

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