Solve the following equation by the square root property. \[ (2 x-2)^{2}=43 \] The solution set is (Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)

Step 1 ：First, we isolate the square root by taking the square root of both sides of the equation. This gives us \(2x-2 = \pm\sqrt{43}\).

Step 2 ：Next, we add 2 to both sides of the equation to isolate \(2x\). This gives us \(2x = 2 \pm\sqrt{43}\).

Step 3 ：Finally, we divide both sides of the equation by 2 to solve for \(x\). This gives us \(x = 1 \pm \frac{\sqrt{43}}{2}\).

Step 4 ：Because we squared the equation, we must check if our solutions are extraneous. For \(x = 1 + \frac{\sqrt{43}}{2}\), the equation reads \((2(1 + \frac{\sqrt{43}}{2})-2)^2 = 43\), which is true. For \(x = 1 - \frac{\sqrt{43}}{2}\), the equation reads \((2(1 - \frac{\sqrt{43}}{2})-2)^2 = 43\), which is also true.

Step 5 ：Therefore, our solutions are \(\boxed{x = 1 + \frac{\sqrt{43}}{2}}\) and \(\boxed{x = 1 - \frac{\sqrt{43}}{2}}\).