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Simplifying 0 = a2 + 12a + 32 Reorder the terms: 0 = 32 + 12a + a2 Solving 0 = 32 + 12a + a2 Solving for variable 'a'. Combine like terms: 0 + -32 = -32 -32 + -12a + -1a2 = 32 + 12a + a2 + -32 + -12a + -1a2 Reorder the terms: -32 + -12a + -1a2 = 32 + -32 + 12a + -12a + a2 + -1a2 Combine like terms: 32 + -32 = 0 -32 + -12a + -1a2 = 0 + 12a + -12a + a2 + -1a2 -32 + -12a + -1a2 = 12a + -12a + a2 + -1a2 Combine like terms: 12a + -12a = 0 -32 + -12a + -1a2 = 0 + a2 + -1a2 -32 + -12a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -32 + -12a + -1a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 12a + a2) = 0 Factor a trinomial. -1((8 + a)(4 + a)) = 0 Ignore the factor -1.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 '(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 = -4Solution
a = {-8, -4}
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