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Simplifying a4 + -8a2 + -16 = 0 Reorder the terms: -16 + -8a2 + a4 = 0 Solving -16 + -8a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8a2 + 16 + a4 = 0 + 16 Reorder the terms: -16 + 16 + -8a2 + a4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8a2 + a4 = 0 + 16 -8a2 + a4 = 0 + 16 Combine like terms: 0 + 16 = 16 -8a2 + a4 = 16 The a term is -8a2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a2 + 16 + a4 = 16 + 16 Reorder the terms: 16 + -8a2 + a4 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8a2 + a4 = 32 Factor a perfect square on the left side: (a2 + -4)(a2 + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (a2 + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
a2 + -4 = 5.656854249 Simplifying a2 + -4 = 5.656854249 Reorder the terms: -4 + a2 = 5.656854249 Solving -4 + a2 = 5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a2 = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + a2 = 5.656854249 + 4 a2 = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 a2 = 9.656854249 Simplifying a2 = 9.656854249 Take the square root of each side: a = {-3.107547948, 3.107547948}Subproblem 2
a2 + -4 = -5.656854249 Simplifying a2 + -4 = -5.656854249 Reorder the terms: -4 + a2 = -5.656854249 Solving -4 + a2 = -5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a2 = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + a2 = -5.656854249 + 4 a2 = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 a2 = -1.656854249 Simplifying a2 = -1.656854249 Reorder the terms: 1.656854249 + a2 = -1.656854249 + 1.656854249 Combine like terms: -1.656854249 + 1.656854249 = 0.000000000 1.656854249 + 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.
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