1. **State the problem:** Solve the quadratic equation $$x^2 + x - 56 = 0$$. 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, $$a=1$$, $$b=1$$, and $$c=-56$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 1^2 - 4 \times 1 \times (-56) = 1 + 224 = 225$$. 5. **Find the square root of the discriminant:** $$\sqrt{225} = 15$$. 6. **Apply the quadratic formula:** $$x = \frac{-1 \pm 15}{2 \times 1} = \frac{-1 \pm 15}{2}$$. 7. **Calculate the two solutions:** - For the plus sign: $$x = \frac{-1 + 15}{2} = \frac{14}{2} = 7$$. - For the minus sign: $$x = \frac{-1 - 15}{2} = \frac{-16}{2} = -8$$. 8. **Final answer:** The solutions to the equation are $$x = 7$$ and $$x = -8$$.