(d) The equation \( (x+2)-3 \sqrt{(x+2)}-4=0 \) has only one real solution. Find the value of \( x \). (Hint: Let \( a=\sqrt{(x+2)}) \)

Solve the equation \( (x+2)-3\sqrt{(x+2)}-4=0 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\left(x+2\right)-3\sqrt{x+2}-4=0\) - step1: Find the domain: \(\left(x+2\right)-3\sqrt{x+2}-4=0,x\geq -2\) - step2: Simplify: \(x-2-3\sqrt{x+2}=0\) - step3: Move the expression to the right-hand side: \(-3\sqrt{x+2}=-x+2\) - step4: Rewrite the expression: \(\sqrt{x+2}=\frac{x-2}{3}\) - step5: Evaluate: \(\sqrt{x+2}=\frac{x-2}{3},\frac{x-2}{3}\geq 0\) - step6: Evaluate: \(\sqrt{x+2}=\frac{x-2}{3},x\geq 2\) - step7: Solve the equation: \(\begin{align}&x=14\\&x=-1\end{align},x\geq 2\) - step8: Find the intersection: \(x=14\) - step9: Check if the solution is in the defined range: \(x=14,x\geq -2\) - step10: Find the intersection: \(x=14\) - step11: Check the solution: \(x=14\) The equation \( (x+2)-3\sqrt{(x+2)}-4=0 \) has only one real solution, which is \( x=14 \).