z 2 + 10z − 24 = 0 What is one of the solutions to the given equation?

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Accepted Answer

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.

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