AHSME 1996 Problem 25

Given that $x^2 + y^2 = 14x + 6y + 6$, what is the largest possible value that $3x + 4y$ can have? $\text{(A)}\ 72 \text{(B)}\ 73 \text{(C)}\ 74 \text{(D)}\ 75 \text{(E)}\ 76$