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Simplifying 24 = 2a2 + 18a + 40 Reorder the terms: 24 = 40 + 18a + 2a2 Solving 24 = 40 + 18a + 2a2 Solving for variable 'a'. Combine like terms: 24 + -40 = -16 -16 + -18a + -2a2 = 40 + 18a + 2a2 + -40 + -18a + -2a2 Reorder the terms: -16 + -18a + -2a2 = 40 + -40 + 18a + -18a + 2a2 + -2a2 Combine like terms: 40 + -40 = 0 -16 + -18a + -2a2 = 0 + 18a + -18a + 2a2 + -2a2 -16 + -18a + -2a2 = 18a + -18a + 2a2 + -2a2 Combine like terms: 18a + -18a = 0 -16 + -18a + -2a2 = 0 + 2a2 + -2a2 -16 + -18a + -2a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 -16 + -18a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(8 + 9a + a2) = 0 Factor a trinomial. -2((8 + a)(1 + a)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve: Simplifying 8 + a = 0 Solving 8 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a = 0 + -8 a = 0 + -8 Combine like terms: 0 + -8 = -8 a = -8 Simplifying a = -8Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-8, -1}
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