Trouble rearranging this equation

[Deceit]

I'm trying to rearrange this equation to isolate r2:

1/2(m2)(v)^2 = [-(G)(m2)(m1)] / (r2) - [-(G)(m2)(m1)] / (r1)

Eliminating m2:
1/2(v)^2 = [-(G)(m1)] / (r2) - [-(G)(m1)] / (r1)

Some swapping around the equal sign:
[(G)(m1)] / (r2) = [(G)(m1)] / (r1) - 1/2(v)^2

Dividing everything by (G)(m1):
1 / (r2) = 1 / (r1) - [(v)^2] / [2(G)(m1)]

Take the reciprocals:
(r2) = (r1) - [2(G)(m1)] / [(v)^2]

This isolates r2, but the answer I get when I substitute the numbers is way off. I'm not 100% confident in my rearranging skills, so I'm pretty sure I've made an error somewhere trying to do so.

So, if someone can point out where I went wrong / which rule of rearranging I may have broken and push me in the right direction, it would be greatly appreciated!

 

[cepheid]

I'm trying to rearrange this equation to isolate r2:

1/2(m2)(v)^2 = [-(G)(m2)(m1)] / (r2) - [-(G)(m2)(m1)] / (r1)

Eliminating m2:
1/2(v)^2 = [-(G)(m1)] / (r2) - [-(G)(m1)] / (r1)

Some swapping around the equal sign:
[(G)(m1)] / (r2) = [(G)(m1)] / (r1) - 1/2(v)^2

Dividing everything by (G)(m1):
1 / (r2) = 1 / (r1) - [(v)^2] / [2(G)(m1)]

Take the reciprocals:
(r2) = (r1) - [2(G)(m1)] / [(v)^2]

This isolates r2, but the answer I get when I substitute the numbers is way off. I'm not 100% confident in my rearranging skills, so I'm pretty sure I've made an error somewhere trying to do so.

So, if someone can point out where I went wrong / which rule of rearranging I may have broken and push me in the right direction, it would be greatly appreciated!

The step in red is way wrong. Before that step, the right hand side of the equation was in the form a - b (it had two terms).

Now, your step assumes that (a-b)^-1 = a^-1 - b^-1. Hopefully it's obvious that this is not true.

Instead, once you get to your second last step, multiply both sides of the equation by r2. Then divide both sides of the equation by all that junk that is multiplying r2 on the right hand side. EDIT: in fact, you can even do that as early as your third last step.

 

[Deceit]

Ah ok; yes that makes complete sense

Thanks for pointing that out :)