Use Vieta's formulas instead of solving the quadratic. For x^2 - (5)x + (-36) = 0, the roots α and β satisfy α + β = 5 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 = (5)^2 - 2(-36) = 25 - (-72) = 97. This is why the correct answer is 97.