An $L=33-$ft$-$long soldier beam is used as a key component of an earth retention system at an excavation site. The soldier beam is subjected to a soil loading that is linearly distributed from $w_A=490l\frac{b}{f}t$ to $w_C=280l\frac{b}{f}t,$ as shown. The soldier beam can be idealized as a cantilever with a fixed support at A$.$ Added support is supplied by a tieback anchor at $B,$ which exerts a force of $P=4200lb$ on the soldier beam at $a=25ft.$ Determine the horizontal deflection of the soldier beam at point $C.$ Assume $EI=4\mathrm{.}5{10}^{8}Ib*in.{?}^2.$