Start by setting: \(u=\sqrt{11-x^2}\\ .\\u-\frac{2}{u}=1\\\)
Rearrange: \(u^2-u-2=0\\.\\(u-2)(u+1)=0\)
So u = 2 or u = -1. However, the original square root must be positive, so only the first value of u is valid.
\(\sqrt{11-x^2}=2\\.\\11-x^2 = 4\\.\\x^2=7\\.\\x=\pm \sqrt7 \)