1. **State the problem:** Solve the quadratic equation $$8)\ 2m^2 - 7m - 13 = -10$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero. $$2m^2 - 7m - 13 + 10 = 0$$ $$2m^2 - 7m - 3 = 0$$ 3. **Factor the quadratic:** Find two numbers that multiply to $2 \times (-3) = -6$ and add to $-7$. These numbers are $-6$ and $-1$. Rewrite the middle term: $$2m^2 - 6m - m - 3 = 0$$ Group terms: $$ (2m^2 - 6m) - (m + 3) = 0$$ Factor each group: $$2m(m - 3) - 1(m + 3) = 0$$ Note the signs do not match for factoring by grouping, so try factoring directly: $$(2m - 1)(m + 3) = 0$$ 4. **Solve each factor:** Set each factor equal to zero: $$2m - 1 = 0 \implies m = \frac{1}{2}$$ $$m + 3 = 0 \implies m = -3$$ 5. **Conclusion:** The solutions to the equation are $$m = \frac{1}{2}$$ and $$m = -3$$. Your solution is correct.