1. **State the problem:** Solve the quadratic equation $$x^2 + 14x - 15 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=14$, and $c=-15$ in this problem. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 14^2 - 4 \times 1 \times (-15) = 196 + 60 = 256$$ 4. **Apply the quadratic formula:** $$x = \frac{-14 \pm \sqrt{256}}{2 \times 1} = \frac{-14 \pm 16}{2}$$ 5. **Find the two solutions:** - For the plus sign: $$x = \frac{-14 + 16}{2} = \frac{2}{2} = 1$$ - For the minus sign: $$x = \frac{-14 - 16}{2} = \frac{-30}{2} = -15$$ 6. **Final answer:** The solutions to the equation are $$x = 1$$ and $$x = -15$$.