Solving a Physics Problem: Struggling with Algebra

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Homework Statement

Ok this was a physics problem...

I'm having a hard time with the algebra part

Homework Equations

solve for X

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

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

 

[Mentallic]

Rather than dealing with all those long and annoying numbers, let's 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.

 

[Architeuthis Dux]

I understand that solving physics problems can be challenging, especially when it involves algebra. It is important to remember that algebra is a fundamental tool in physics and mastering it will greatly benefit your problem-solving skills. In this particular problem, I can see that you have made progress and are on the right track. However, I would suggest double-checking your calculations and equations to ensure accuracy. It may also be helpful to break down the problem into smaller steps and use the given equations and variables to guide your solution. Don't be discouraged if it takes some time to solve, as practice and persistence are key in mastering any subject. Keep up the good work and don't hesitate to seek help from a teacher or peer if needed.