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Simplifying 40a4 + 48a2 + -16 = 0 Reorder the terms: -16 + 48a2 + 40a4 = 0 Solving -16 + 48a2 + 40a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8'. 8(-2 + 6a2 + 5a4) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + 6a2 + 5a4)' equal to zero and attempt to solve: Simplifying -2 + 6a2 + 5a4 = 0 Solving -2 + 6a2 + 5a4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 1.2a2 + a4 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.2a2 + 0.4 + a4 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.2a2 + a4 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.2a2 + a4 = 0 + 0.4 1.2a2 + a4 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.2a2 + a4 = 0.4 The a term is 1.2a2. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2a2 + 0.36 + a4 = 0.4 + 0.36 Reorder the terms: 0.36 + 1.2a2 + a4 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + 1.2a2 + a4 = 0.76 Factor a perfect square on the left side: (a2 + 0.6)(a2 + 0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (a2 + 0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
a2 + 0.6 = 0.871779789 Simplifying a2 + 0.6 = 0.871779789 Reorder the terms: 0.6 + a2 = 0.871779789 Solving 0.6 + a2 = 0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + a2 = 0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + a2 = 0.871779789 + -0.6 a2 = 0.871779789 + -0.6 Combine like terms: 0.871779789 + -0.6 = 0.271779789 a2 = 0.271779789 Simplifying a2 = 0.271779789 Take the square root of each side: a = {-0.521325032, 0.521325032}Subproblem 2
a2 + 0.6 = -0.871779789 Simplifying a2 + 0.6 = -0.871779789 Reorder the terms: 0.6 + a2 = -0.871779789 Solving 0.6 + a2 = -0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + a2 = -0.871779789 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + a2 = -0.871779789 + -0.6 a2 = -0.871779789 + -0.6 Combine like terms: -0.871779789 + -0.6 = -1.471779789 a2 = -1.471779789 Simplifying a2 = -1.471779789 Reorder the terms: 1.471779789 + a2 = -1.471779789 + 1.471779789 Combine like terms: -1.471779789 + 1.471779789 = 0.000000000 1.471779789 + a2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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