Homework Help: Algebra Help

1. Dec 23, 2009

GreenPrint

1. The problem statement, all variables and given/known data

Ok this was a physics problem...

I'm having a hard time with the algebra part

2. Relevant equations

solve for X

7.35E22/(3.84403E8 - X)^2 = 5.98E24/X^2

3. The attempt at a solution

i have got down to this and I think it is right but it might be wrong

0 = (7.35E22 X^2)/5.98E24 - X^2 + 2(3.84403E8)X - (3.84403E8)^2

2. Dec 23, 2009

Mentallic

Rather than dealing with all those long and annoying numbers, lets assign letters to stand for them, and we can substitute back after all the algebra is done.

Let:
$$A=7.35x10^{22}$$
$$B=3.84403x10^8$$
$$C=5.98x10^{24}$$

So now we have $$\frac{A}{(B-X)^2}=\frac{C}{X^2}$$

You want to get rid of the fractions, so you need to multiply by the higher common factor, which is $X^2(B-X)^2$

Then you'll get $$AX^2=C(B-X)^2$$

Now you need to expand, move everything to one side and let the equation = 0 and collect like terms. You should get it in the form $mx^2+nx+p=0$ where m, n and p are all some constant, and x is the variable that you're trying to solve.

Now you can apply the quadratic formula.