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Simplifying 2a3 + a2 + 5a + 7a3 + 8a2 + 2a = 0 Reorder the terms: 5a + 2a + a2 + 8a2 + 2a3 + 7a3 = 0 Combine like terms: 5a + 2a = 7a 7a + a2 + 8a2 + 2a3 + 7a3 = 0 Combine like terms: a2 + 8a2 = 9a2 7a + 9a2 + 2a3 + 7a3 = 0 Combine like terms: 2a3 + 7a3 = 9a3 7a + 9a2 + 9a3 = 0 Solving 7a + 9a2 + 9a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(7 + 9a + 9a2) = 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 '(7 + 9a + 9a2)' equal to zero and attempt to solve: Simplifying 7 + 9a + 9a2 = 0 Solving 7 + 9a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + a + a2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + a + -0.7777777778 + a2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + a + a2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + a + a2 = 0 + -0.7777777778 a + a2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 a + a2 = -0.7777777778 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = -0.7777777778 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = -0.7777777778 + 0.25 Combine like terms: -0.7777777778 + 0.25 = -0.5277777778 1.25 + a2 = -0.5277777778 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.5277777778 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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