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Simplifying -12a8 + -12a6 + -36a4 = 0 Reorder the terms: -36a4 + -12a6 + -12a8 = 0 Solving -36a4 + -12a6 + -12a8 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-12a4'. -12a4(3 + a2 + a4) = 0 Ignore the factor -12.Subproblem 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 + a2 + a4)' equal to zero and attempt to solve: Simplifying 3 + a2 + a4 = 0 Solving 3 + a2 + a4 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + a2 + -3 + a4 = 0 + -3 Reorder the terms: 3 + -3 + a2 + a4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a2 + a4 = 0 + -3 a2 + a4 = 0 + -3 Combine like terms: 0 + -3 = -3 a2 + a4 = -3 The a term is a2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a2 + 0.25 + a4 = -3 + 0.25 Reorder the terms: 0.25 + a2 + a4 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + a2 + a4 = -2.75 Factor a perfect square on the left side: (a2 + 0.5)(a2 + 0.5) = -2.75 Can't calculate square root of the right side. 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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