z^2 +10z−24 = 0 What is one of the solutions to the given equation?
Correct answer: 2 (parsed from the explanation — this source omits an answer key for this item)
Explanation
-12 The correct answer is either 2 or . The left-hand side of the given equation -24 10 can be rewritten by factoring. The two values that multiply to and add to 12 - are and 2. It follows that the given equation can be rewritten as +12 -2 =0 +12=0 ^z h^z h . Setting each factor equal to 0 yields two equations: z -2=0 12 +12=0 and z . Subtracting from both sides of the equation z results in =-12 -2=0 = z . Adding 2 to both sides of the equation z results in z 2. Note that 2 and -12 are examples of ways to enter a correct answer.
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