1. **State the problem:** Solve the quadratic equation $$m^2 + 2m - 3 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the equation. 3. **Identify coefficients:** Here, $a = 1$, $b = 2$, and $c = -3$. 4. **Calculate the discriminant:** $$b^2 - 4ac = 2^2 - 4(1)(-3) = 4 + 12 = 16$$ 5. **Apply the quadratic formula:** $$m = \frac{-2 \pm \sqrt{16}}{2(1)} = \frac{-2 \pm 4}{2}$$ 6. **Simplify each solution:** - For the plus sign: $$m = \frac{-2 + 4}{2} = \frac{2}{2} = 1$$ - For the minus sign: $$m = \frac{-2 - 4}{2} = \frac{-6}{2} = -3$$ 7. **Final answer:** The solutions are $$m = 1$$ and $$m = -3$$.