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Simplifying 10a3 + 7a2 + 1a = 0 Reorder the terms: 1a + 7a2 + 10a3 = 0 Solving 1a + 7a2 + 10a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(1 + 7a + 10a2) = 0 Factor a trinomial. a((1 + 2a)(1 + 5a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 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 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Subproblem 3
Set the factor '(1 + 5a)' equal to zero and attempt to solve: Simplifying 1 + 5a = 0 Solving 1 + 5a = 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 + 5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5a = 0 + -1 5a = 0 + -1 Combine like terms: 0 + -1 = -1 5a = -1 Divide each side by '5'. a = -0.2 Simplifying a = -0.2Solution
a = {0, -0.5, -0.2}
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