Find the larger of the two distinct solutions to the equation $$x^2 - 11x - 42 = 0.$$
To find the solutions to a quadratic equation, I can try to factor it or use the quadratic formula. I notice that the equation has integer coefficients, so factoring might be easier. I look for two numbers that multiply to -42 and add to -11. I see that -14 and 3 are such numbers, so I can write the equation as $$x^2 - 11x - 42 = (x - 14)(x + 3) = 0.$$ Now, by the zero product property, either x - 14 = 0 or x + 3 = 0. So the solutions are x = 14 or x = -3. The larger of the two solutions is x = 14. 