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Simplifying 12a5 + 30a3 + -30a = 0 Reorder the terms: -30a + 30a3 + 12a5 = 0 Solving -30a + 30a3 + 12a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6a'. 6a(-5 + 5a2 + 2a4) = 0 Ignore the factor 6.Subproblem 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 '(-5 + 5a2 + 2a4)' equal to zero and attempt to solve: Simplifying -5 + 5a2 + 2a4 = 0 Solving -5 + 5a2 + 2a4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 2.5a2 + a4 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.5a2 + 2.5 + a4 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.5a2 + a4 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.5a2 + a4 = 0 + 2.5 2.5a2 + a4 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.5a2 + a4 = 2.5 The a term is 2.5a2. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5a2 + 1.5625 + a4 = 2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5a2 + a4 = 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + 2.5a2 + a4 = 4.0625 Factor a perfect square on the left side: (a2 + 1.25)(a2 + 1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (a2 + 1.25) equal to 2.015564437 and -2.015564437.Subproblem 1
a2 + 1.25 = 2.015564437 Simplifying a2 + 1.25 = 2.015564437 Reorder the terms: 1.25 + a2 = 2.015564437 Solving 1.25 + a2 = 2.015564437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a2 = 2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a2 = 2.015564437 + -1.25 a2 = 2.015564437 + -1.25 Combine like terms: 2.015564437 + -1.25 = 0.765564437 a2 = 0.765564437 Simplifying a2 = 0.765564437 Take the square root of each side: a = {-0.874965392, 0.874965392}Subproblem 2
a2 + 1.25 = -2.015564437 Simplifying a2 + 1.25 = -2.015564437 Reorder the terms: 1.25 + a2 = -2.015564437 Solving 1.25 + a2 = -2.015564437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a2 = -2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a2 = -2.015564437 + -1.25 a2 = -2.015564437 + -1.25 Combine like terms: -2.015564437 + -1.25 = -3.265564437 a2 = -3.265564437 Simplifying a2 = -3.265564437 Reorder the terms: 3.265564437 + a2 = -3.265564437 + 3.265564437 Combine like terms: -3.265564437 + 3.265564437 = 0.000000000 3.265564437 + a2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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