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Simplifying (5a + 10) * a = -5 Reorder the terms: (10 + 5a) * a = -5 Reorder the terms for easier multiplication: a(10 + 5a) = -5 (10 * a + 5a * a) = -5 (10a + 5a2) = -5 Solving 10a + 5a2 = -5 Solving for variable 'a'. Reorder the terms: 5 + 10a + 5a2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 10a + 5a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 2a + a2) = 0 Factor a trinomial. 5((1 + a)(1 + a)) = 0 Ignore the factor 5.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 + 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 = -1Solution
a = {-1, -1}
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