Use Vieta's formulas instead of solving the quadratic. For x^2 - (10)x + (25) = 0, the roots α and β satisfy α + β = 10 and αβ = 25. 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 = (10)^2 - 2(25) = 100 - (50) = 50. This is why the correct answer is 50.