Solve by completing the square. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) \[ v^{2}+6 v+1=0 \] \( v=\square \)

Solve the equation \( v^{2}+6v+1=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(v^{2}+6v+1=0\) - step1: Solve using the quadratic formula: \(v=\frac{-6\pm \sqrt{6^{2}-4}}{2}\) - step2: Simplify the expression: \(v=\frac{-6\pm \sqrt{32}}{2}\) - step3: Simplify the expression: \(v=\frac{-6\pm 4\sqrt{2}}{2}\) - step4: Separate into possible cases: \(\begin{align}&v=\frac{-6+4\sqrt{2}}{2}\\&v=\frac{-6-4\sqrt{2}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&v=-3+2\sqrt{2}\\&v=\frac{-6-4\sqrt{2}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&v=-3+2\sqrt{2}\\&v=-3-2\sqrt{2}\end{align}\) - step7: Rewrite: \(v_{1}=-3-2\sqrt{2},v_{2}=-3+2\sqrt{2}\) The solutions to the equation \(v^{2}+6v+1=0\) by completing the square are \(v=-3-2\sqrt{2}\) and \(v=-3+2\sqrt{2}\).