Solve the following quadratic function by completing the square. \[ y=x^{2}+4 x-2 \]

Solve the equation \( x^{2}+4x-2=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}+4x-2=0\) - step1: Solve using the quadratic formula: \(x=\frac{-4\pm \sqrt{4^{2}-4\left(-2\right)}}{2}\) - step2: Simplify the expression: \(x=\frac{-4\pm \sqrt{24}}{2}\) - step3: Simplify the expression: \(x=\frac{-4\pm 2\sqrt{6}}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{-4+2\sqrt{6}}{2}\\&x=\frac{-4-2\sqrt{6}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=-2+\sqrt{6}\\&x=\frac{-4-2\sqrt{6}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=-2+\sqrt{6}\\&x=-2-\sqrt{6}\end{align}\) - step7: Rewrite: \(x_{1}=-2-\sqrt{6},x_{2}=-2+\sqrt{6}\) The solutions to the quadratic function \(y=x^{2}+4x-2\) by completing the square are \(x=-2-\sqrt{6}\) and \(x=-2+\sqrt{6}\).