I'm doing a physics problem and I'm stuck on something that should be easy by now but yet I can't figure out how to solve this neatly. I've tried completing the square and the quadratic formula but the results get really ugly.
The two unknowns are $v_a'$ and $v_b'$ but I only need $v_b'$. According to the notes the answer should be
I don't see how $v_a'$ vanishes here. The answer I got was
Any help is welcome.