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Simplifying 20a4 + 17a3 + 3a2 = 0 Reorder the terms: 3a2 + 17a3 + 20a4 = 0 Solving 3a2 + 17a3 + 20a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a2'. a2(3 + 17a + 20a2) = 0 Factor a trinomial. a2((3 + 5a)(1 + 4a)) = 0Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve: Simplifying 3 + 5a = 0 Solving 3 + 5a = 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 + 5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5a = 0 + -3 5a = 0 + -3 Combine like terms: 0 + -3 = -3 5a = -3 Divide each side by '5'. a = -0.6 Simplifying a = -0.6Subproblem 3
Set the factor '(1 + 4a)' equal to zero and attempt to solve: Simplifying 1 + 4a = 0 Solving 1 + 4a = 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 + 4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4a = 0 + -1 4a = 0 + -1 Combine like terms: 0 + -1 = -1 4a = -1 Divide each side by '4'. a = -0.25 Simplifying a = -0.25Solution
a = {0, -0.6, -0.25}
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