# Trouble rearranging this equation

• Deceit
In summary, the conversation involves someone trying to rearrange an equation to isolate r2. They make a mistake in one of their steps and ask for help in finding where they went wrong. The correct step is pointed out, which involves multiplying both sides by r2 and dividing by the other terms on the right hand side.
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!

Deceit said:
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.

Ah ok; yes that makes complete sense

Thanks for pointing that out :)

## What does it mean to "rearrange" an equation?

Rearranging an equation means to manipulate the terms and symbols in the equation in order to isolate a specific variable or make the equation easier to solve.

## Why would someone need to rearrange an equation?

Rearranging an equation can help simplify the problem and make it easier to understand and solve. It can also help to isolate a specific variable and make it easier to find its value.

## What are the basic rules for rearranging equations?

The basic rules for rearranging equations include maintaining equality by performing the same operation on both sides of the equation, combining like terms, and isolating the desired variable by moving all other terms to the opposite side of the equation.

## What are the common mistakes people make when rearranging equations?

Common mistakes when rearranging equations include forgetting to perform the same operation on both sides, incorrectly combining like terms, and forgetting to switch the sign when moving a term to the opposite side of the equation.

## What are some tips for effectively rearranging equations?

Some tips for effectively rearranging equations include keeping track of operations and signs, simplifying the equation as much as possible before rearranging, and double-checking your work to ensure the equation is still balanced after rearranging.

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