Solving a quadratic equation by completing the square: Exact... Solve the quadratic equation by completing the square. \[ x^{2}+12 x+22=0 \] First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: \[ \begin{array}{l}0(x+\square)^{2}=\square \\ (x-\square)^{2}=\square\end{array} \] Solution:

Step 1 ：The given quadratic equation is in the form of \(ax^2 + bx + c = 0\). To solve this equation by completing the square, we need to rewrite the equation in the form of \((x + p)^2 = q\), where \(p = \frac{b}{2a}\) and \(q = c - \frac{b^2}{4a}\). Then, we can solve for \(x\) by taking the square root of both sides of the equation.

Step 2 ：In this case, \(a = 1\), \(b = 12\), and \(c = 22\). So, \(p = \frac{12}{2*1} = 6\) and \(q = 22 - \frac{12^2}{4*1} = -14\). Therefore, the equation can be rewritten as \((x + 6)^2 = -14\).

Step 3 ：Next, we solve for \(x\) by taking the square root of both sides of the equation. Since the right side of the equation is negative, the solutions will be complex numbers. The solutions are \(x = -6 \pm \sqrt{-14}\), which can be simplified to \(x = -6 \pm \sqrt{14}i\), where \(i\) is the imaginary unit.

Step 4 ：Final Answer: The solutions to the quadratic equation \(x^{2}+12 x+22=0\) are \(\boxed{x = -6 + 3.74i}\) and \(\boxed{x = -6 - 3.74i}\).