1. **State the problem:** Solve the quadratic equation $$x^2 - 7x + 10 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a=1$$, $$b=-7$$, and $$c=10$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-7)^2 - 4 \times 1 \times 10 = 49 - 40 = 9$$. 5. **Find the square root of the discriminant:** $$\sqrt{9} = 3$$. 6. **Apply the quadratic formula:** $$x = \frac{-(-7) \pm 3}{2 \times 1} = \frac{7 \pm 3}{2}$$. 7. **Calculate the two solutions:** - $$x_1 = \frac{7 + 3}{2} = \frac{10}{2} = 5$$ - $$x_2 = \frac{7 - 3}{2} = \frac{4}{2} = 2$$ **Final answer:** The solutions to the equation are $$x = 5$$ and $$x = 2$$.