\( 2 \sqrt{x-5}=2 \), solve for \( x \)

Solve the equation \( 2\sqrt{x-5}=2 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2\sqrt{x-5}=2\) - step1: Find the domain: \(2\sqrt{x-5}=2,x\geq 5\) - step2: Divide both sides: \(\frac{2\sqrt{x-5}}{2}=\frac{2}{2}\) - step3: Divide the numbers: \(\sqrt{x-5}=1\) - step4: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{x-5}\right)^{2}=1^{2}\) - step5: Evaluate the power: \(x-5=1\) - step6: Move the constant to the right side: \(x=1+5\) - step7: Add the numbers: \(x=6\) - step8: Check if the solution is in the defined range: \(x=6,x\geq 5\) - step9: Find the intersection: \(x=6\) - step10: Check the solution: \(x=6\) The solution to the equation \(2\sqrt{x-5}=2\) is \(x=6\).