Use Vieta's formulas instead of solving the quadratic. For x^2 - (-12)x + (36) = 0, the roots α and β satisfy α + β = -12 and αβ = 36. The expression we need is α^2 + β^2. Use the identity α^2 + β^2 = (α + β)^2 - 2αβ. So α^2 + β^2 = (-12)^2 - 2(36) = 144 - (72) = 72. This is why the correct answer is 72.