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Simplifying 5a + -37 = a2 + 21a + 27 Reorder the terms: -37 + 5a = a2 + 21a + 27 Reorder the terms: -37 + 5a = 27 + 21a + a2 Solving -37 + 5a = 27 + 21a + a2 Solving for variable 'a'. Reorder the terms: -37 + -27 + 5a + -21a + -1a2 = 27 + 21a + a2 + -27 + -21a + -1a2 Combine like terms: -37 + -27 = -64 -64 + 5a + -21a + -1a2 = 27 + 21a + a2 + -27 + -21a + -1a2 Combine like terms: 5a + -21a = -16a -64 + -16a + -1a2 = 27 + 21a + a2 + -27 + -21a + -1a2 Reorder the terms: -64 + -16a + -1a2 = 27 + -27 + 21a + -21a + a2 + -1a2 Combine like terms: 27 + -27 = 0 -64 + -16a + -1a2 = 0 + 21a + -21a + a2 + -1a2 -64 + -16a + -1a2 = 21a + -21a + a2 + -1a2 Combine like terms: 21a + -21a = 0 -64 + -16a + -1a2 = 0 + a2 + -1a2 -64 + -16a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -64 + -16a + -1a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(64 + 16a + a2) = 0 Factor a trinomial. -1((8 + a)(8 + 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 '(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 = {-8, -8}
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