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Simplifying a5 + -28a3 + -27a = 0 Reorder the terms: -27a + -28a3 + a5 = 0 Solving -27a + -28a3 + a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-27 + -28a2 + a4) = 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 '(-27 + -28a2 + a4)' equal to zero and attempt to solve: Simplifying -27 + -28a2 + a4 = 0 Solving -27 + -28a2 + a4 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -28a2 + 27 + a4 = 0 + 27 Reorder the terms: -27 + 27 + -28a2 + a4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -28a2 + a4 = 0 + 27 -28a2 + a4 = 0 + 27 Combine like terms: 0 + 27 = 27 -28a2 + a4 = 27 The a term is -28a2. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28a2 + 196 + a4 = 27 + 196 Reorder the terms: 196 + -28a2 + a4 = 27 + 196 Combine like terms: 27 + 196 = 223 196 + -28a2 + a4 = 223 Factor a perfect square on the left side: (a2 + -14)(a2 + -14) = 223 Calculate the square root of the right side: 14.933184523 Break this problem into two subproblems by setting (a2 + -14) equal to 14.933184523 and -14.933184523.Subproblem 1
a2 + -14 = 14.933184523 Simplifying a2 + -14 = 14.933184523 Reorder the terms: -14 + a2 = 14.933184523 Solving -14 + a2 = 14.933184523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a2 = 14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + a2 = 14.933184523 + 14 a2 = 14.933184523 + 14 Combine like terms: 14.933184523 + 14 = 28.933184523 a2 = 28.933184523 Simplifying a2 = 28.933184523 Take the square root of each side: a = {-5.378957568, 5.378957568}Subproblem 2
a2 + -14 = -14.933184523 Simplifying a2 + -14 = -14.933184523 Reorder the terms: -14 + a2 = -14.933184523 Solving -14 + a2 = -14.933184523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a2 = -14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + a2 = -14.933184523 + 14 a2 = -14.933184523 + 14 Combine like terms: -14.933184523 + 14 = -0.933184523 a2 = -0.933184523 Simplifying a2 = -0.933184523 Reorder the terms: 0.933184523 + a2 = -0.933184523 + 0.933184523 Combine like terms: -0.933184523 + 0.933184523 = 0.000000000 0.933184523 + 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.Solution
a = {0}
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