OG详解-OG9 数学2 Q14

The correct answer is either 2 or -12. The left-hand side of the given equation can be rewritten by factoring. The two values that multiply to -24 and add to 10 are 12 and -2. It follows that the given equation can be rewritten as (z+12)(z-2) = 0. Setting each factor equal to 0 yields two equations: z+12 = 0 and z-2 = 0. Subtracting 12 from both sides of the equation z+12 = 0 results in z =-12. Adding 2 to both sides of the equation z-2 = 0 results in z = 2. Note that 2 and -12 are examples of ways to enter a correct answer.