Use Vieta's formulas instead of solving the quadratic. For x^2 - (-6)x + (5) = 0, the roots α and β satisfy α + β = -6 and αβ = 5. 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 = (-6)^2 - 2(5) = 36 - (10) = 26. This is why the correct answer is 26.