Original: Averaged across the entire sample, molecular collisions can be regarded as essentially elastic as long as black-body photons are not permitted to carry away energy from the system.
Simplified: frac {3 \* 4 ^ 2} 2 + frac {5 \* (-6) ^ 2} 2 = frac {3 (-8.5) ^ 2} 2 + frac {5v ^ 2} 2