Solve for \( x \) by completing the square: \( x^{2}-4 x+2=0 \)

To solve the equation \( x^2 - 4x + 2 = 0 \) by completing the square, we first move the constant to the other side, giving us \( x^2 - 4x = -2 \). Next, we take half of the coefficient of \( x \) (which is -4), square it, and add it to both sides. Half of -4 is -2, and squaring it gives us 4. So we add 4 to both sides: \[ x^2 - 4x + 4 = -2 + 4 \] This simplifies to: \[ (x - 2)^2 = 2 \] Now, we take the square root of both sides: \[ x - 2 = \pm\sqrt{2} \] Finally, we solve for \( x \): \[ x = 2 \pm \sqrt{2} \] Thus, the solutions are: \[ x = 2 + \sqrt{2} \quad \text{and} \quad x = 2 - \sqrt{2} \]