11. \( m^{2}+8 m+15=0 \)

To solve the quadratic equation \( m^{2}+8 m+15=0 \), you can factor it. Look for two numbers that multiply to 15 and add up to 8. These numbers are 3 and 5. Thus, the equation factors to \( (m + 3)(m + 5) = 0 \). Setting each factor to zero gives you the solutions \( m = -3 \) and \( m = -5 \). Easy peasy! For a different approach, you can use the quadratic formula: \( m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). In this case, \( a = 1, b = 8, c = 15 \). Plugging the values into the formula yields the same results: \( m = -3 \) and \( m = -5 \). This method always works, regardless of whether the quadratic can be factored. Give it a try next time!