+53 Guest, that is wrong.
We have \(\sqrt{x} + 2 = \sqrt{x+100}\). Squaring both sides, we have \(x+4+4\sqrt{x}=x+100\). Combining like terms, we get \(4\sqrt{x}=96\), thus \(\sqrt{x}=24.\) So we have \(\boxed{x=24^2=576.}\) Plugging this in, we see see that it is a solution to the equation. \(\square\)
