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.
This is very effective online webpage.
I simply entered the equation in the form
300x^2 -16.667x^3-7200 = 0
http://www.wolframalpha.com/input/?i=300x%5E2+-16.667x%5E3-7200+%3D0
It gave my 3 real answers and the corresponding gram of
f(x) = 300x^2 -16.667x^3-7200
Let the 16.667 be treated at 16 2/3. Then
900 x^2 -50 x^3 -21600 = 0
One root of that equation is exactly x = 6. Call it a lucky guess.
Divide the cubic by (x-6) to get an easily solved quadratic, for the other two roots. It can be reduced to
x^2 -120 x -72 = 0
To solve the equation 300x^2 - 16.667x^3 = 7200, you can use a method called "factoring" or "finding roots". Here's how you can approach it step by step:
Step 1: Re-arrange the equation in the standard form, which means moving all terms to one side to make it equal to zero:
16.667x^3 - 300x^2 + 7200 = 0
Step 2: Factor out the common factor, if any. In this case, you can factor out 1 to simplify the equation:
1 * (16.667x^3 - 300x^2 + 7200) = 0
Step 3: Try to factorize the remaining expression. In this case, the expression is a cubic polynomial, which can be quite challenging to factorize. You could try different factoring techniques, such as factoring by grouping, but it might be difficult in this case.
Step 4: If factoring seems difficult, you can use numerical methods to approximate the solutions. One popular method is the Newton-Raphson method. However, this method requires advanced mathematical knowledge and might not be suitable for this scenario.
In summary, factoring a cubic polynomial can be quite challenging, and in some cases, it might not be possible to find exact solutions. In such situations, numerical methods or approximation techniques can be used to find approximate values for the roots.