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Simplifying a2 + 12a + 89 = 9 + -6a Reorder the terms: 89 + 12a + a2 = 9 + -6a Solving 89 + 12a + a2 = 9 + -6a Solving for variable 'a'. Reorder the terms: 89 + -9 + 12a + 6a + a2 = 9 + -6a + -9 + 6a Combine like terms: 89 + -9 = 80 80 + 12a + 6a + a2 = 9 + -6a + -9 + 6a Combine like terms: 12a + 6a = 18a 80 + 18a + a2 = 9 + -6a + -9 + 6a Reorder the terms: 80 + 18a + a2 = 9 + -9 + -6a + 6a Combine like terms: 9 + -9 = 0 80 + 18a + a2 = 0 + -6a + 6a 80 + 18a + a2 = -6a + 6a Combine like terms: -6a + 6a = 0 80 + 18a + a2 = 0 Factor a trinomial. (10 + a)(8 + a) = 0Subproblem 1
Set the factor '(10 + a)' equal to zero and attempt to solve: Simplifying 10 + a = 0 Solving 10 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + a = 0 + -10 a = 0 + -10 Combine like terms: 0 + -10 = -10 a = -10 Simplifying a = -10Subproblem 2
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 = -8Solution
a = {-10, -8}
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