1. **State the problem:** Solve the quadratic expression $m^2 - 10m - 11 = 0$ for $m$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solutions are given by $$m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-10$, and $c=-11$ in this case. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-10)^2 - 4 \times 1 \times (-11) = 100 + 44 = 144$$ 4. **Apply the quadratic formula:** $$m = \frac{-(-10) \pm \sqrt{144}}{2 \times 1} = \frac{10 \pm 12}{2}$$ 5. **Find the two solutions:** - For the plus sign: $$m = \frac{10 + 12}{2} = \frac{22}{2} = 11$$ - For the minus sign: $$m = \frac{10 - 12}{2} = \frac{\cancel{10} - \cancel{12}}{\cancel{2}} = \frac{-2}{2} = -1$$ 6. **Final answer:** The solutions to the equation $m^2 - 10m - 11 = 0$ are $$m = 11 \quad \text{or} \quad m = -1$$