Solve equation for d: Rewriting Physics Homework

[1MileCrash]

Homework Statement

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

Homework Equations

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?

 

[SammyS]

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.

 

[1MileCrash]

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]

How about scanning that solution & posting the image?

 

[1MileCrash]

Sure thing, gimme a few minutes.

 

[1MileCrash]

http://img585.imageshack.us/img585/5854/physicsstone.png

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

 

[SammyS]

It's just a typo.

It could be (1 ÷ v²) d²

The following lines appear to be correct.