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Simplifying a2 + 7a + 27 = 9 + -2a Reorder the terms: 27 + 7a + a2 = 9 + -2a Solving 27 + 7a + a2 = 9 + -2a Solving for variable 'a'. Reorder the terms: 27 + -9 + 7a + 2a + a2 = 9 + -2a + -9 + 2a Combine like terms: 27 + -9 = 18 18 + 7a + 2a + a2 = 9 + -2a + -9 + 2a Combine like terms: 7a + 2a = 9a 18 + 9a + a2 = 9 + -2a + -9 + 2a Reorder the terms: 18 + 9a + a2 = 9 + -9 + -2a + 2a Combine like terms: 9 + -9 = 0 18 + 9a + a2 = 0 + -2a + 2a 18 + 9a + a2 = -2a + 2a Combine like terms: -2a + 2a = 0 18 + 9a + a2 = 0 Factor a trinomial. (6 + a)(3 + a) = 0Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve: Simplifying 6 + a = 0 Solving 6 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + a = 0 + -6 a = 0 + -6 Combine like terms: 0 + -6 = -6 a = -6 Simplifying a = -6Subproblem 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 = {-6, -3}
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