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Simplifying 6a8 + 10a6 + -3a4 = 0 Reorder the terms: -3a4 + 10a6 + 6a8 = 0 Solving -3a4 + 10a6 + 6a8 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a4'. a4(-3 + 10a2 + 6a4) = 0Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve: Simplifying a4 = 0 Solving a4 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + 10a2 + 6a4)' equal to zero and attempt to solve: Simplifying -3 + 10a2 + 6a4 = 0 Solving -3 + 10a2 + 6a4 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 1.666666667a2 + a4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.666666667a2 + 0.5 + a4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.666666667a2 + a4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.666666667a2 + a4 = 0 + 0.5 1.666666667a2 + a4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.666666667a2 + a4 = 0.5 The a term is 1.666666667a2. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667a2 + 0.6944444447 + a4 = 0.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667a2 + a4 = 0.5 + 0.6944444447 Combine like terms: 0.5 + 0.6944444447 = 1.1944444447 0.6944444447 + 1.666666667a2 + a4 = 1.1944444447 Factor a perfect square on the left side: (a2 + 0.8333333335)(a2 + 0.8333333335) = 1.1944444447 Calculate the square root of the right side: 1.092906421 Break this problem into two subproblems by setting (a2 + 0.8333333335) equal to 1.092906421 and -1.092906421.Subproblem 1
a2 + 0.8333333335 = 1.092906421 Simplifying a2 + 0.8333333335 = 1.092906421 Reorder the terms: 0.8333333335 + a2 = 1.092906421 Solving 0.8333333335 + a2 = 1.092906421 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + a2 = 1.092906421 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + a2 = 1.092906421 + -0.8333333335 a2 = 1.092906421 + -0.8333333335 Combine like terms: 1.092906421 + -0.8333333335 = 0.2595730875 a2 = 0.2595730875 Simplifying a2 = 0.2595730875 Take the square root of each side: a = {-0.509483157, 0.509483157}Subproblem 2
a2 + 0.8333333335 = -1.092906421 Simplifying a2 + 0.8333333335 = -1.092906421 Reorder the terms: 0.8333333335 + a2 = -1.092906421 Solving 0.8333333335 + a2 = -1.092906421 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + a2 = -1.092906421 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + a2 = -1.092906421 + -0.8333333335 a2 = -1.092906421 + -0.8333333335 Combine like terms: -1.092906421 + -0.8333333335 = -1.9262397545 a2 = -1.9262397545 Simplifying a2 = -1.9262397545 Reorder the terms: 1.9262397545 + a2 = -1.9262397545 + 1.9262397545 Combine like terms: -1.9262397545 + 1.9262397545 = 0.0000000000 1.9262397545 + a2 = 0.0000000000 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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