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 \[ \begin{array}{c}\text { Form: } \\ \quad(x+\square)^{2}=\square \\ (x-\square)^{2}=\square\end{array} \]

To solve the quadratic equation \( x^{2} - 2x - 12 = 0 \) by completing the square, we first need to rearrange the equation: 1. Move the constant term to the other side: \[ x^{2} - 2x = 12 \] 2. Now, we will complete the square on the left side. Take half of the coefficient of \( x \) (which is -2), square it, and add it to both sides: \[ \left(-\frac{2}{2}\right)^{2} = (-1)^{2} = 1 \] Therefore, we add 1 to both sides: \[ x^{2} - 2x + 1 = 12 + 1 \] \[ (x - 1)^{2} = 13 \] So, filling in the blanks we have: \[ (x - 1)^{2} = 13 \] 3. Now, let's solve for \( x \) by taking the square root of both sides: \[ x - 1 = \pm \sqrt{13} \] Hence, \[ x = 1 + \sqrt{13} \quad \text{or} \quad x = 1 - \sqrt{13} \] So the solutions are: \[ x = 1 + \sqrt{13}, \quad x = 1 - \sqrt{13} \]