Use Vieta's formulas instead of solving the quadratic. For x^2 - (-7)x + (-60) = 0, the roots α and β satisfy α + β = -7 and αβ = -60. 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 = (-7)^2 - 2(-60) = 49 - (-120) = 169. This is why the correct answer is 169.