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Simplifying a2 + 3a + 20 = 8 + -4a Reorder the terms: 20 + 3a + a2 = 8 + -4a Solving 20 + 3a + a2 = 8 + -4a Solving for variable 'a'. Reorder the terms: 20 + -8 + 3a + 4a + a2 = 8 + -4a + -8 + 4a Combine like terms: 20 + -8 = 12 12 + 3a + 4a + a2 = 8 + -4a + -8 + 4a Combine like terms: 3a + 4a = 7a 12 + 7a + a2 = 8 + -4a + -8 + 4a Reorder the terms: 12 + 7a + a2 = 8 + -8 + -4a + 4a Combine like terms: 8 + -8 = 0 12 + 7a + a2 = 0 + -4a + 4a 12 + 7a + a2 = -4a + 4a Combine like terms: -4a + 4a = 0 12 + 7a + a2 = 0 Factor a trinomial. (4 + a)(3 + a) = 0Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Solution
a = {-4, -3}
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