(c) $\sqrt{x+110}=x$

Step 1 ：The given equation is \(\sqrt{x+110}=x\).

Step 2 ：To solve this equation, we need to square both sides to eliminate the square root.

Step 3 ：Squaring both sides, we get \(x = x\).

Step 4 ：Solving this equation, we find that \(x = 11\).

Step 5 ：However, when solving radical equations, it's important to check the solution in the original equation, because squaring both sides can sometimes introduce extraneous solutions.

Step 6 ：Substituting \(x = 11\) back into the original equation, we find that it holds true.

Step 7 ：Therefore, the solution to the equation \(\sqrt{x+110}=x\) is \(\boxed{11}\).