jmc

Since the vertex of the parabola is $(3,7)$, the parabola is symmetric around the line $x=3$. Furthermore, the two $x$-intercepts of the parabola are also symmetric around this line. One $x$-intercept is $(-2,0)$, whose distance from the line $x=3$ is $3-(-2)=5$, so the other $x$-intercept is at $(3+5,0)=(8,0)$. The $x$-coordinate of this $x$-intercept is $\boxed{8}$.