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Simplifying 2a3 + -18a2 + 13a = 0 Reorder the terms: 13a + -18a2 + 2a3 = 0 Solving 13a + -18a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(13 + -18a + 2a2) = 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 '(13 + -18a + 2a2)' equal to zero and attempt to solve: Simplifying 13 + -18a + 2a2 = 0 Solving 13 + -18a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -9a + a2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -9a + -6.5 + a2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -9a + a2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -9a + a2 = 0 + -6.5 -9a + a2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -9a + a2 = -6.5 The a term is -9a. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9a + 20.25 + a2 = -6.5 + 20.25 Reorder the terms: 20.25 + -9a + a2 = -6.5 + 20.25 Combine like terms: -6.5 + 20.25 = 13.75 20.25 + -9a + a2 = 13.75 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (a + -4.5) equal to 3.708099244 and -3.708099244.Subproblem 1
a + -4.5 = 3.708099244 Simplifying a + -4.5 = 3.708099244 Reorder the terms: -4.5 + a = 3.708099244 Solving -4.5 + a = 3.708099244 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 3.708099244 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 3.708099244 + 4.5 a = 3.708099244 + 4.5 Combine like terms: 3.708099244 + 4.5 = 8.208099244 a = 8.208099244 Simplifying a = 8.208099244Subproblem 2
a + -4.5 = -3.708099244 Simplifying a + -4.5 = -3.708099244 Reorder the terms: -4.5 + a = -3.708099244 Solving -4.5 + a = -3.708099244 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -3.708099244 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -3.708099244 + 4.5 a = -3.708099244 + 4.5 Combine like terms: -3.708099244 + 4.5 = 0.791900756 a = 0.791900756 Simplifying a = 0.791900756Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.208099244, 0.791900756}Solution
a = {0, 8.208099244, 0.791900756}
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