# Rewriting equation

## Homework Statement

This is for a physics problem. I need to solve this for d, but I'm not sure how.

## The Attempt at a Solution

I've gotten up to:

$\frac{2d}{g} = (t - \frac{d}{v})^{2}$

When I multiply the right term out, it becomes a mess, everything I do makes it ugly. What should I try doing?

My main source of confusion is that multiplying that out gives me:

$t^{2} - \frac{2dt}{v} + \frac{d^{2}}{v^{2}}$

While my solution manual gives the last term as:

(1+v^2)d^2.

Those are not the same. What gives?

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## Answers and Replies

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SammyS
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If squaring the right hand side makes it too ugly for you, then try taking the square root of both sides. That makes the math a little more challenging,

You could multiply both sides by v2 then square the right hand side. Maybe not quite so ugly.

If squaring the right hand side makes it too ugly for you, then try taking the square root of both sides. That makes the math a little more challenging,

You could multiply both sides by v2 then square the right hand side. Maybe not quite so ugly.
My main problem is that the solution manual I have gives steps that I just don't follow.

They multiply out (t-d/v)^2 and get (1+v^2)d^2 for the last term. I literally haven't the slightest how it comes to that, I just get plain old d^2/v^2.. and they aren't the same.

SammyS
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How about scanning that solution & posting the image?

Sure thing, gimme a few minutes.

http://img585.imageshack.us/img585/5854/physicsstone.png [Broken]

After "square both sides to obtain.." I don't know how they get that. At all.

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SammyS
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It's just a typo.

It could be (1 ÷ v2) d2

The following lines appear to be correct.