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Simplifying 2a2 + 3a2 + 4a3 + 2a = 0 Reorder the terms: 2a + 2a2 + 3a2 + 4a3 = 0 Combine like terms: 2a2 + 3a2 = 5a2 2a + 5a2 + 4a3 = 0 Solving 2a + 5a2 + 4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(2 + 5a + 4a2) = 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 + 5a + 4a2)' equal to zero and attempt to solve: Simplifying 2 + 5a + 4a2 = 0 Solving 2 + 5a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 1.25a + a2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.25a + -0.5 + a2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.25a + a2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.25a + a2 = 0 + -0.5 1.25a + a2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.25a + a2 = -0.5 The a term is 1.25a. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25a + 0.390625 + a2 = -0.5 + 0.390625 Reorder the terms: 0.390625 + 1.25a + a2 = -0.5 + 0.390625 Combine like terms: -0.5 + 0.390625 = -0.109375 0.390625 + 1.25a + a2 = -0.109375 Factor a perfect square on the left side: (a + 0.625)(a + 0.625) = -0.109375 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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