I figured out a solution to a recurrence relation, but I’m not sure what the constant should be for the last step to hold.

$ T(n)= 5T(n/4) + n^2$

Guess: $ T(n) = O(n^2)$

Prove: $ T(n) \leq cn^2 $

Breakdown

$ T(n) \leq 5(c(n/4)^2) + n^2 $

$ = (5/16)cn^2 + n^2 $

$ \leq cn^2 $

For the last step to hold I’m not sure what the value of c should be because of the (5/16). My guess would be c >= 1 and I’m not sure if that would hold.