This is easy man :v you just double it up ~`~

\(1+\sqrt{2x}=10\)

Condition \(x\ge0\)

\(\Leftrightarrow\sqrt{2x}=9\)

\(\Leftrightarrow\left(\sqrt{2x}\right)^2=9^2\)

\(\Leftrightarrow2x=81\left(2x\ge0\right)\)

\(\Rightarrow x=\dfrac{81}{2}\) (satisfy with condition)

Hence, \(S=\left\{\dfrac{81}{2}\right\}\)