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Simplifying 83a3 + -18a2 + 4a = 2a Reorder the terms: 4a + -18a2 + 83a3 = 2a Solving 4a + -18a2 + 83a3 = 2a Solving for variable 'a'. Reorder the terms: 4a + -2a + -18a2 + 83a3 = 2a + -2a Combine like terms: 4a + -2a = 2a 2a + -18a2 + 83a3 = 2a + -2a Combine like terms: 2a + -2a = 0 2a + -18a2 + 83a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(2 + -18a + 83a2) = 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 '(2 + -18a + 83a2)' equal to zero and attempt to solve: Simplifying 2 + -18a + 83a2 = 0 Solving 2 + -18a + 83a2 = 0 Begin completing the square. Divide all terms by 83 the coefficient of the squared term: Divide each side by '83'. 0.02409638554 + -0.2168674699a + a2 = 0 Move the constant term to the right: Add '-0.02409638554' to each side of the equation. 0.02409638554 + -0.2168674699a + -0.02409638554 + a2 = 0 + -0.02409638554 Reorder the terms: 0.02409638554 + -0.02409638554 + -0.2168674699a + a2 = 0 + -0.02409638554 Combine like terms: 0.02409638554 + -0.02409638554 = 0.00000000000 0.00000000000 + -0.2168674699a + a2 = 0 + -0.02409638554 -0.2168674699a + a2 = 0 + -0.02409638554 Combine like terms: 0 + -0.02409638554 = -0.02409638554 -0.2168674699a + a2 = -0.02409638554 The a term is -0.2168674699a. Take half its coefficient (-0.108433735). Square it (0.01175787489) and add it to both sides. Add '0.01175787489' to each side of the equation. -0.2168674699a + 0.01175787489 + a2 = -0.02409638554 + 0.01175787489 Reorder the terms: 0.01175787489 + -0.2168674699a + a2 = -0.02409638554 + 0.01175787489 Combine like terms: -0.02409638554 + 0.01175787489 = -0.01233851065 0.01175787489 + -0.2168674699a + a2 = -0.01233851065 Factor a perfect square on the left side: (a + -0.108433735)(a + -0.108433735) = -0.01233851065 Can't calculate square root of the right side. 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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