Use the square root property to solve the equation. \[ (x-11)^{2}=19 \] The solution set is \( \left\{\begin{array}{l}\text {. }\end{array}\right. \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Solve the equation \( (x-11)^{2}=19 \). Solve the quadratic equation by following steps: - step0: Solve using square roots: \(\left(x-11\right)^{2}=19\) - step1: Simplify the expression: \(x-11=\pm \sqrt{19}\) - step2: Separate into possible cases: \(\begin{align}&x-11=\sqrt{19}\\&x-11=-\sqrt{19}\end{align}\) - step3: Move the constant to the right side: \(\begin{align}&x=\sqrt{19}+11\\&x=-\sqrt{19}+11\end{align}\) - step4: Rewrite: \(x_{1}=-\sqrt{19}+11,x_{2}=\sqrt{19}+11\) The solution set for the equation \((x-11)^{2}=19\) using the square root property is \(x = -\sqrt{19} + 11\) or \(x = \sqrt{19} + 11\).