3.73: Tangent meets axes; mid-point of $XY$

The tangent to the curve $y = \mathrm{e}^{x}(2x + 5)^{\frac{1}{2}}$ at the point where $x = 2$ meets the $x$-axis at the point $X$ and the $y$-axis at the point $Y$. Find the coordinates of the mid-point of $XY$, giving your answer in exact form.