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Simplifying 6a3 + a2 + 5a + 2a3 + 4a2 + 3a = 0 Reorder the terms: 5a + 3a + a2 + 4a2 + 6a3 + 2a3 = 0 Combine like terms: 5a + 3a = 8a 8a + a2 + 4a2 + 6a3 + 2a3 = 0 Combine like terms: a2 + 4a2 = 5a2 8a + 5a2 + 6a3 + 2a3 = 0 Combine like terms: 6a3 + 2a3 = 8a3 8a + 5a2 + 8a3 = 0 Solving 8a + 5a2 + 8a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(8 + 5a + 8a2) = 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 '(8 + 5a + 8a2)' equal to zero and attempt to solve: Simplifying 8 + 5a + 8a2 = 0 Solving 8 + 5a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + 0.625a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.625a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 0.625a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.625a + a2 = 0 + -1 0.625a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.625a + a2 = -1 The a term is 0.625a. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625a + 0.09765625 + a2 = -1 + 0.09765625 Reorder the terms: 0.09765625 + 0.625a + a2 = -1 + 0.09765625 Combine like terms: -1 + 0.09765625 = -0.90234375 0.09765625 + 0.625a + a2 = -0.90234375 Factor a perfect square on the left side: (a + 0.3125)(a + 0.3125) = -0.90234375 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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