a) \( x^{2}=2(x+12) \)

To solve the equation \( x^{2}=2(x+12) \), we can start by expanding the right-hand side: \( x^{2} = 2x + 24 \). Next, we move everything to one side to set the equation to zero: \( x^{2} - 2x - 24 = 0 \). Now, we can factor this quadratic equation. It factors as \( (x - 6)(x + 4) = 0 \). Setting each factor to zero gives us the solutions: \( x = 6 \) and \( x = -4 \). Double-checking these with the original equation shows they both satisfy it. So, there you have it! The solutions are \( x = 6 \) and \( x = -4 \). Now go ahead and plug these numbers into your original equation to see them in action!