\( \sqrt{16 x+41}=x+6 \) The solution set is

Solve the equation \( \sqrt{16x+41}=x+6 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\sqrt{16x+41}=x+6\) - step1: Find the domain: \(\sqrt{16x+41}=x+6,x\geq -\frac{41}{16}\) - step2: Evaluate: \(\sqrt{16x+41}=x+6,x+6\geq 0\) - step3: Evaluate: \(\sqrt{16x+41}=x+6,x\geq -6\) - step4: Solve the equation: \(\begin{align}&x=5\\&x=-1\end{align},x\geq -6\) - step5: Find the intersection: \(\begin{align}&x=5\\&x=-1\end{align}\) - step6: Check if the solution is in the defined range: \(\begin{align}&x=5\\&x=-1\end{align},x\geq -\frac{41}{16}\) - step7: Find the intersection: \(\begin{align}&x=5\\&x=-1\end{align}\) - step8: Check the solution: \(\begin{align}&x=5\\&x=-1\end{align}\) - step9: Rewrite: \(x_{1}=-1,x_{2}=5\) The solution set for the equation \( \sqrt{16x+41}=x+6 \) is \( x=-1 \) and \( x=5 \).