Use Vieta's formulas instead of solving the quadratic. For x^2 - (7)x + (-30) = 0, the roots α and β satisfy α + β = 7 and αβ = -30. 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(-30) = 49 - (-60) = 109. This is why the correct answer is 109.