Solve the equation using the quadratic formula. \[ x^{2}-12 x+61=0 \] The solution set is \( \} \). (Simplity your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to se answers as needed.)

To solve the equation \( x^{2}-12x+61=0 \) using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \), we first identify \( a = 1 \), \( b = -12 \), and \( c = 61 \). Calculating the discriminant: \[ b^2 - 4ac = (-12)^2 - 4(1)(61) = 144 - 244 = -100 \] Since the discriminant is negative, we have complex roots. Now substituting into the quadratic formula: \[ x = \frac{-(-12) \pm \sqrt{-100}}{2(1)} = \frac{12 \pm 10i}{2} \] This simplifies to: \[ x = 6 \pm 5i \] Thus, the solution set is \( \{ 6 + 5i, 6 - 5i \} \).