The angles in a particular triangle are in arithmetic progression, and the side lengths are $4,5,x$. The sum of the possible values of x equals $a+\sqrt{b}+\sqrt{c}$ where $a, b$, and $c$ are positive integers. What is $a+b+c$? $\textbf{(A)}\ 36\qquad$ $\textbf{(B)}\ 38\qquad$ $\textbf{(C)}\ 40\qquad$ $\textbf{(D)}\ 42\qquad$ $\textbf{(E)}\ 44$