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Simplifying 28a + -5a3 + -3a2 = 0 Reorder the terms: 28a + -3a2 + -5a3 = 0 Solving 28a + -3a2 + -5a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(28 + -3a + -5a2) = 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 '(28 + -3a + -5a2)' equal to zero and attempt to solve: Simplifying 28 + -3a + -5a2 = 0 Solving 28 + -3a + -5a2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.6 + 0.6a + a2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 0.6a + 5.6 + a2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 0.6a + a2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 0.6a + a2 = 0 + 5.6 0.6a + a2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 0.6a + a2 = 5.6 The a term is 0.6a. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6a + 0.09 + a2 = 5.6 + 0.09 Reorder the terms: 0.09 + 0.6a + a2 = 5.6 + 0.09 Combine like terms: 5.6 + 0.09 = 5.69 0.09 + 0.6a + a2 = 5.69 Factor a perfect square on the left side: (a + 0.3)(a + 0.3) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (a + 0.3) equal to 2.385372088 and -2.385372088.Subproblem 1
a + 0.3 = 2.385372088 Simplifying a + 0.3 = 2.385372088 Reorder the terms: 0.3 + a = 2.385372088 Solving 0.3 + a = 2.385372088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + a = 2.385372088 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + a = 2.385372088 + -0.3 a = 2.385372088 + -0.3 Combine like terms: 2.385372088 + -0.3 = 2.085372088 a = 2.085372088 Simplifying a = 2.085372088Subproblem 2
a + 0.3 = -2.385372088 Simplifying a + 0.3 = -2.385372088 Reorder the terms: 0.3 + a = -2.385372088 Solving 0.3 + a = -2.385372088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + a = -2.385372088 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + a = -2.385372088 + -0.3 a = -2.385372088 + -0.3 Combine like terms: -2.385372088 + -0.3 = -2.685372088 a = -2.685372088 Simplifying a = -2.685372088Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.085372088, -2.685372088}Solution
a = {0, 2.085372088, -2.685372088}
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