1. **Problem:** Solve for real $x$ in the quadratic equation $$x^2 - 7x + 10 = 0.$$ 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the roots are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$$ 3. **Apply formula:** Here, $a=1$, $b=-7$, $c=10$. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-7)^2 - 4 \times 1 \times 10 = 49 - 40 = 9.$$ 4. **Find roots:** Since $\Delta > 0$, two distinct real roots exist: $$x = \frac{-(-7) \pm \sqrt{9}}{2 \times 1} = \frac{7 \pm 3}{2}.$$ 5. **Calculate each root:** - Root 1: $$x = \frac{7 + 3}{2} = \frac{10}{2} = 5.$$ - Root 2: $$x = \frac{7 - 3}{2} = \frac{4}{2} = 2.$$ 6. **Answer:** The roots are $x=2$ and $x=5$. **Correct choice:** A. 2,5