There's a part in the solution that I can't understand, I think it's just something basic that I'm missing. In the solution it says:
$$T(k) \leq 2(c(k/2)^2 \log(k/2)) + k^2$$
Then it became
$$T(k) \leq ( ck^2 \log(k/2) ) / 2 + k^2$$
P.S: I forgot how to do StackExchange latex again, I am so sorry.