Use Vieta's formulas instead of solving the quadratic. For x^2 - (-8)x + (-33) = 0, the roots α and β satisfy α + β = -8 and αβ = -33. 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 = (-8)^2 - 2(-33) = 64 - (-66) = 130. This is why the correct answer is 130.