Hapi, the god of the annual flooding of the Nile, is preparing for this year's flooding. The shape of the channel of the Nile can be described by the function $y = \frac{-1000}{x^2+100}$, where the $x$ and $y$ coordinates are in meters. The current depth of the river is $5$ meters. Hapi plans to increase the water level by $3$ meters. How many meters wide will the river be after the flooding? The depth of the river is always measured at its deepest point.

Let's think step by step and output the final answer within \boxed{}.
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