Final answer:
The most efficient method to solve the quadratic equation x² + 12x + 35 = 0 is by factoring it into (x + 5)(x + 7), resulting in two solutions: x = -5 and x = -7.
Step-by-step explanation:
The most efficient technique for solving x² + 12x + 35 = 0 is by factoring. This quadratic equation can be factored as (x + 5)(x + 7) = 0. To solve for x, we set each factor equal to zero: x + 5 = 0, giving us x = -5, and x + 7 = 0, giving us x = -7. Therefore, the solutions to the equation are x = -5 and x = -7.