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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

z 2 + 10 z - 24 = 0

What is one of the solutions to the given equation?

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Explanation

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+12z-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.