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Simplifying a4 + 10a2 + -16 = 0 Reorder the terms: -16 + 10a2 + a4 = 0 Solving -16 + 10a2 + 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 + 10a2 + 16 + a4 = 0 + 16 Reorder the terms: -16 + 16 + 10a2 + a4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 10a2 + a4 = 0 + 16 10a2 + a4 = 0 + 16 Combine like terms: 0 + 16 = 16 10a2 + a4 = 16 The a term is 10a2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a2 + 25 + a4 = 16 + 25 Reorder the terms: 25 + 10a2 + a4 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + 10a2 + a4 = 41 Factor a perfect square on the left side: (a2 + 5)(a2 + 5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (a2 + 5) equal to 6.403124237 and -6.403124237.Subproblem 1
a2 + 5 = 6.403124237 Simplifying a2 + 5 = 6.403124237 Reorder the terms: 5 + a2 = 6.403124237 Solving 5 + a2 = 6.403124237 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a2 = 6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + a2 = 6.403124237 + -5 a2 = 6.403124237 + -5 Combine like terms: 6.403124237 + -5 = 1.403124237 a2 = 1.403124237 Simplifying a2 = 1.403124237 Take the square root of each side: a = {-1.184535452, 1.184535452}Subproblem 2
a2 + 5 = -6.403124237 Simplifying a2 + 5 = -6.403124237 Reorder the terms: 5 + a2 = -6.403124237 Solving 5 + a2 = -6.403124237 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a2 = -6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + a2 = -6.403124237 + -5 a2 = -6.403124237 + -5 Combine like terms: -6.403124237 + -5 = -11.403124237 a2 = -11.403124237 Simplifying a2 = -11.403124237 Reorder the terms: 11.403124237 + a2 = -11.403124237 + 11.403124237 Combine like terms: -11.403124237 + 11.403124237 = 0.000000000 11.403124237 + 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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