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Simplifying 2a3 + 3a2 + -8a = 0 Reorder the terms: -8a + 3a2 + 2a3 = 0 Solving -8a + 3a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-8 + 3a + 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 '(-8 + 3a + 2a2)' equal to zero and attempt to solve: Simplifying -8 + 3a + 2a2 = 0 Solving -8 + 3a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 1.5a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.5a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 1.5a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.5a + a2 = 0 + 4 1.5a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.5a + a2 = 4 The a term is 1.5a. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5a + 0.5625 + a2 = 4 + 0.5625 Reorder the terms: 0.5625 + 1.5a + a2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + 1.5a + a2 = 4.5625 Factor a perfect square on the left side: (a + 0.75)(a + 0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (a + 0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
a + 0.75 = 2.136000936 Simplifying a + 0.75 = 2.136000936 Reorder the terms: 0.75 + a = 2.136000936 Solving 0.75 + a = 2.136000936 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 2.136000936 + -0.75 a = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 a = 1.386000936 Simplifying a = 1.386000936Subproblem 2
a + 0.75 = -2.136000936 Simplifying a + 0.75 = -2.136000936 Reorder the terms: 0.75 + a = -2.136000936 Solving 0.75 + a = -2.136000936 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -2.136000936 + -0.75 a = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 a = -2.886000936 Simplifying a = -2.886000936Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.386000936, -2.886000936}Solution
a = {0, 1.386000936, -2.886000936}
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