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Simplifying 7 + -3a(a + 1) = 8 + a Reorder the terms: 7 + -3a(1 + a) = 8 + a 7 + (1 * -3a + a * -3a) = 8 + a 7 + (-3a + -3a2) = 8 + a Solving 7 + -3a + -3a2 = 8 + a Solving for variable 'a'. Reorder the terms: 7 + -8 + -3a + -1a + -3a2 = 8 + a + -8 + -1a Combine like terms: 7 + -8 = -1 -1 + -3a + -1a + -3a2 = 8 + a + -8 + -1a Combine like terms: -3a + -1a = -4a -1 + -4a + -3a2 = 8 + a + -8 + -1a Reorder the terms: -1 + -4a + -3a2 = 8 + -8 + a + -1a Combine like terms: 8 + -8 = 0 -1 + -4a + -3a2 = 0 + a + -1a -1 + -4a + -3a2 = a + -1a Combine like terms: a + -1a = 0 -1 + -4a + -3a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 4a + 3a2) = 0 Factor a trinomial. -1((1 + a)(1 + 3a)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve: Simplifying 1 + 3a = 0 Solving 1 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333Solution
a = {-1, -0.3333333333}
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