Solving for Velocity: Kinetic Energy and Rest Energy Relationship Explained

[chris_0101]

Homework Statement

I need help solving for velocity from the equation K = [(mc^2)/sqrt(1-((v^2)/(c^2))] - mc^2

Homework Equations

K = [(mc^2)/sqrt(1-((v^2)/(c^2))] - mc^2

where mc^2 is the rest energy​

K is the kinetic energy​

The Attempt at a Solution

K = [(mc^2)/sqrt(1-((v^2)/(c^2))] - mc^2
K[sqrt(1-((v^2)/(c^2))] = (mc^2) - mc^2
sqrt(1-((v^2)/(c^2)) = [mc^2 - mc^2] / K
1-((v^2)/(c^2)) = [(mc^2 - mc^2)/K]^2
v = sqrt(1-c^2[[(mc^2 - mc^2)/K]^2] ------ final answer

However, my textbook has a different answer, which is:
v = c(sqrt(1 - [1 / (1 +K/mc^2)^2]))

Any help will be greatly appreciated, Thanks

 

[JesseC]

K = [(mc^2)/sqrt(1-((v^2)/(c^2))] - mc^2
K[sqrt(1-((v^2)/(c^2))] = (mc^2) - mc^2 <------------ HERE

On the second line, for forgot to multiply -mc^2 by [sqrt(1-((v^2)/(c^2))].
It should be K[sqrt(1-((v^2)/(c^2))] = (mc^2) - mc^2[sqrt(1-((v^2)/(c^2))]

 

[chris_0101]

Thanks, it worked out now