Solve the equation. \( \begin{array}{c}\sqrt{2 x+10}-2 \sqrt{x}=0 \\ x=[?]\end{array} \)

To solve the equation \( \sqrt{2x + 10} - 2\sqrt{x} = 0 \), let's first isolate the square root: \[ \sqrt{2x + 10} = 2\sqrt{x} \] Next, we square both sides to eliminate the square root: \[ 2x + 10 = 4x \] Now, rearranging gives us: \[ 10 = 4x - 2x \quad \Rightarrow \quad 10 = 2x \quad \Rightarrow \quad x = 5 \] Finally, we can check if \( x = 5 \) satisfies the original equation: \[ \sqrt{2(5) + 10} - 2\sqrt{5} = \sqrt{10 + 10} - 2\sqrt{5} = \sqrt{20} - 2\sqrt{5} \] Since \( \sqrt{20} = 2\sqrt{5} \), we have \( 2\sqrt{5} - 2\sqrt{5} = 0 \), which is true. Thus, the solution is: \[ x = 5 \]