# Solving for a variable help :)

by MathiasArendru
Tags: solving, variable
 P: 12 Hey guys, this is a little silly question but it bothers me. Im not a math genius (yet i hope) and im still in elementary school so theres alot to learn. But i just read about the lorenz factor in this example he basically used pythagoras of this light clock in a train, so it started of as $$(ct)^2 = (cx)^2 + (vt)^2$$ and he derived it into: $$t = \frac{x}{\sqrt{1-\frac{v^2}{c^2}}}$$ I would have posted an attemp to solve it but i really just dont know how to crack it and get started Pleeeaaase help it would be really nice :D
 Mentor P: 12,037 That is nothing you can derive (at least not in the way you ask for here), that is a definition of γ.
 P: 12 right its me god im stupid! he solved for t not gamma dont really know what went through my head while i wrote it. i corrected it in the post now
 Mentor P: 18,346 Solving for a variable help :) OK, I'll help you get started: bring all terms which have a ##t## to one side of the equation and the other terms on the other side. Isolate ##t^2## so you have ##t^2 = \text{something}##. Then take roots.
 P: 12 ok ill try: $c^2t^2 = c^2x^2 + v^2t^2$ $t^2 = \frac{c^2x^2 + v^2t^2}{c^2}$ Dividing both sides by t^2 $1 = \frac{c^2x^2 + v^2t^2}{c^2t^2}$ im stuck... lol normally i dont really have trouble when solving for variables but this one irritates me.. can i have another hint ? :)
Mentor
P: 18,346
 Quote by MathiasArendru ok ill try: $c^2t^2 = c^2x^2 + v^2t^2$ $t^2 = \frac{c^2x^2 + v^2t^2}{c^2}$
I can see a ##t^2## on the LHS and on the RHS. The idea is to have all occurences of ##t^2## on the LHS.
 P: 12 Exacly thats the though part, because normally i would just divide out the t^2 but that wont help in this example as it would leave me with a 1 on the LHS.. and that wouldnt help much,, is there some mechanism or method that i am missing that could solve this? i feel like theres something i havent learned that could allow this to be solved.. or is it just me thats blind?
Mentor
P: 18,346
 Quote by MathiasArendru Exacly thats the though part, because normally i would just divide out the t^2 but that wont help in this example as it would leave me with a 1 on the LHS.. and that wouldnt help much,, is there some mechanism or method that i am missing that could solve this? i feel like theres something i havent learned that could allow this to be solved.. or is it just me thats blind?
If you have ##2x^2 = 5 - 3x^2##, can you solve that? You just need to do the same thing here. Isolate ##x##.
 P: 12 Yea no problem but there i can just add 3x^2 to both sides, in my example its $v^2t^2$ so i cant do the same thing here?
Mentor
P: 3,926
 Quote by MathiasArendru Yea no problem but there i can just add 3x^2 to both sides, in my example its $v^2t^2$ so i cant do the same thing here?
You could try subtracting ##v^2t^2## from both sides.
 Quote by MathiasArendru Yea no problem but there i can just add 3x^2 to both sides, in my example its $v^2t^2$ so i cant do the same thing here?