1. **State the problem:** We are given the quadratic equation $$x^2 - 5x + 4 = 0$$ and its two real solutions $$x_1 < x_2$$. We need to compute the value of $$x_1 + 2x_2$$. 2. **Recall the quadratic formula and sum/product of roots:** For a quadratic equation $$ax^2 + bx + c = 0$$, the sum of roots is $$x_1 + x_2 = -\frac{b}{a}$$ and the product of roots is $$x_1 x_2 = \frac{c}{a}$$. 3. **Apply to our equation:** Here, $$a=1$$, $$b=-5$$, and $$c=4$$. Sum of roots: $$x_1 + x_2 = -\frac{-5}{1} = 5$$ Product of roots: $$x_1 x_2 = \frac{4}{1} = 4$$ 4. **Find the roots explicitly (optional for clarity):** Using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{5 \pm \sqrt{25 - 16}}{2} = \frac{5 \pm 3}{2}$$ So, $$x_1 = \frac{5 - 3}{2} = 1$$ $$x_2 = \frac{5 + 3}{2} = 4$$ 5. **Compute the required expression:** $$x_1 + 2x_2 = 1 + 2 \times 4 = 1 + 8 = 9$$ **Final answer:** $$9$$