ii) Hence, solve the equation \( \frac{8}{\sqrt{x}-5}-\sqrt{x}=0 \).

Solve the equation \( \frac{8}{\sqrt{x}-5}-\sqrt{x}=0 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{8}{\sqrt{x}-5}-\sqrt{x}=0\) - step1: Find the domain: \(\frac{8}{\sqrt{x}-5}-\sqrt{x}=0,x \in \left[0,25\right)\cup \left(25,+\infty\right)\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{8}{\sqrt{x}-5}-\sqrt{x}\right)\left(\sqrt{x}-5\right)=0\times \left(\sqrt{x}-5\right)\) - step3: Simplify the equation: \(8-x+5\sqrt{x}=0\) - step4: Move the expression to the right-hand side: \(5\sqrt{x}=-8+x\) - step5: Rewrite the expression: \(\sqrt{x}=\frac{-8+x}{5}\) - step6: Evaluate: \(\sqrt{x}=\frac{-8+x}{5},\frac{-8+x}{5}\geq 0\) - step7: Evaluate: \(\sqrt{x}=\frac{-8+x}{5},x\geq 8\) - step8: Solve the equation: \(\begin{align}&x=\frac{41+5\sqrt{57}}{2}\\&x=\frac{41-5\sqrt{57}}{2}\end{align},x\geq 8\) - step9: Find the intersection: \(x=\frac{41+5\sqrt{57}}{2}\) - step10: Check if the solution is in the defined range: \(x=\frac{41+5\sqrt{57}}{2},x \in \left[0,25\right)\cup \left(25,+\infty\right)\) - step11: Find the intersection: \(x=\frac{41+5\sqrt{57}}{2}\) - step12: Check the solution: \(x=\frac{41+5\sqrt{57}}{2}\) The solution to the equation \( \frac{8}{\sqrt{x}-5}-\sqrt{x}=0 \) is \( x=\frac{41+5\sqrt{57}}{2} \).