\( 8=12+\sqrt{2-2 x} \) The siluton set is \( \square \).

To solve the equation \( 8=12+\sqrt{2-2 x} \), start by isolating the square root. Subtract 12 from both sides to get \( -4=\sqrt{2-2 x} \). Since the square root cannot equal a negative number, there are no real solutions, meaning the solution set is empty: \( \emptyset \). Now, let's talk about the reality of square roots! Did you know that square roots reveal the beauty of numbers, like how the square root of 9 is 3 because 3 times 3 equals 9? But be wary; that root can’t take on negative values—it's all about the positivity! Have you heard of complex numbers? They extend the number system by introducing imaginary units like \( i \), where \( i^2 = -1 \). If you ever encounter situations with negative roots, those complex numbers can save the day and allow for all sorts of exciting mathematical explorations!