Finding initial velocity of two elementary particles

[asilvester635]

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I'm not sure how they got the extra (1/2)mv^2? My question is shown using pink font in the image below as well as my attempt.

 

[Doc Al]

I'm not sure how they got the extra (1/2)mv^2?

There are two particles so you must consider the KE of both. (Note that in the figure both particles end up with zero final velocity.)