posted by Kari on .
Hi this is a dimensional analysis problem,I want to solve for x.
I really don't know what to do.
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.
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
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.