1. **State the problem:** Solve the quadratic equation $$m^2 - 5m - 14 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a$$, $$b$$, and $$c$$ are coefficients. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -5$$, and $$c = -14$$. 4. **Calculate the discriminant:** $$D = b^2 - 4ac = (-5)^2 - 4 \times 1 \times (-14) = 25 + 56 = 81$$ 5. **Apply the quadratic formula:** $$m = \frac{-(-5) \pm \sqrt{81}}{2 \times 1} = \frac{5 \pm 9}{2}$$ 6. **Find the two solutions:** - For the plus sign: $$m = \frac{5 + 9}{2} = \frac{14}{2} = 7$$ - For the minus sign: $$m = \frac{5 - 9}{2} = \frac{-4}{2} = -2$$ 7. **Final answer:** The solutions are $$m = 7$$ and $$m = -2$$. --- **Graph:** The quadratic function is $$y = m^2 - 5m - 14$$. The parabola opens upwards (since $$a=1 > 0$$) and crosses the x-axis at $$m = 7$$ and $$m = -2$$. --- **Summary:** The solutions to $$m^2 - 5m - 14 = 0$$ are $$m = 7$$ and $$m = -2$$.