Solve the quadratic equation by completi \[ x^{2}-2 x-12=0 \] First, choose the appropriate form and fill numbers. Then, solve the equation. Simplify your a If there is more than one solution, separa \[ \begin{array}{c}\text { Form: } \\ \quad(x+\square)^{2}=\square \\ (x-\square)^{2}=\square\end{array} \]

Solve the equation \( x^{2}-2x-12=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}-2x-12=0\) - step1: Solve using the quadratic formula: \(x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\left(-12\right)}}{2}\) - step2: Simplify the expression: \(x=\frac{2\pm \sqrt{52}}{2}\) - step3: Simplify the expression: \(x=\frac{2\pm 2\sqrt{13}}{2}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{2+2\sqrt{13}}{2}\\&x=\frac{2-2\sqrt{13}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&x=1+\sqrt{13}\\&x=\frac{2-2\sqrt{13}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&x=1+\sqrt{13}\\&x=1-\sqrt{13}\end{align}\) - step7: Rewrite: \(x_{1}=1-\sqrt{13},x_{2}=1+\sqrt{13}\) The solutions to the quadratic equation \(x^{2}-2x-12=0\) by completing the square are \(x_{1}=1-\sqrt{13}\) and \(x_{2}=1+\sqrt{13}\).