Solve the equation by completing the square: \( x^{2}-12 x+56=3 \) \( \begin{array}{l}-6-\sqrt{17} i,-6+\sqrt{17} i \\ -6+17 i,-6-17 i \\ 6-17 i, 6+17 i \\ 0-\sqrt{17} i, 6+\sqrt{17} i \\ -17-\sqrt{3} i,-17+\sqrt{3} i\end{array} \)

To solve the equation \( x^{2}-12 x+56=3 \) by completing the square, we start by rearranging it: 1. Move all terms to one side: \[ x^{2} - 12x + 56 - 3 = 0 \quad \Rightarrow \quad x^{2} - 12x + 53 = 0 \] 2. Next, isolate the quadratic and linear terms: \[ x^{2} - 12x = -53 \] 3. Complete the square on the left side. Take half of the coefficient of \( x \) (which is \(-12\)), square it, and add to both sides: \[ x^{2} - 12x + 36 = -53 + 36 \quad \Rightarrow \quad (x - 6)^{2} = -17 \] 4. Solve for \( x - 6 \) by taking the square root: \[ x - 6 = \pm \sqrt{-17} = \pm i\sqrt{17} \] 5. Finally, solve for \( x \): \[ x = 6 \pm i\sqrt{17} \] Hence, the solutions are: \[ 6 - i\sqrt{17} \quad \text{and} \quad 6 + i\sqrt{17} \] It looks like the options provided contain two solutions for \( x \); the correct representation would be \( \boxed{6 \pm i\sqrt{17}} \).