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.
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.
To solve for x in the equation 300x^2 - 16.667x^3 = 7200, we can follow a step-by-step process:
Step 1: Rearrange the equation to set it equal to zero:
300x^2 - 16.667x^3 - 7200 = 0
Step 2: Factor out the common factor, if possible:
0 = x^2(300 - 16.667x) - 7200
0 = x^2(300 - 16.667x - 24)
Step 3: Simplify the equation:
0 = x^2(275.333 - 16.667x)
Step 4: Apply the zero product property:
Either x^2 = 0 or 275.333 - 16.667x = 0
Step 5: Solve for x in each equation:
x^2 = 0: This gives us the solution x = 0.
275.333 - 16.667x = 0: Subtract 275.333 from both sides to get -16.667x = -275.333. Then divide by -16.667 to solve for x, which gives us x ≈ 16.52.
So the two solutions to the equation are x = 0 and x ≈ 16.52.