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Simplifying a4 + -12a2 + -16 = 0 Reorder the terms: -16 + -12a2 + a4 = 0 Solving -16 + -12a2 + 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 + -12a2 + 16 + a4 = 0 + 16 Reorder the terms: -16 + 16 + -12a2 + a4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -12a2 + a4 = 0 + 16 -12a2 + a4 = 0 + 16 Combine like terms: 0 + 16 = 16 -12a2 + a4 = 16 The a term is -12a2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a2 + 36 + a4 = 16 + 36 Reorder the terms: 36 + -12a2 + a4 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + -12a2 + a4 = 52 Factor a perfect square on the left side: (a2 + -6)(a2 + -6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (a2 + -6) equal to 7.211102551 and -7.211102551.Subproblem 1
a2 + -6 = 7.211102551 Simplifying a2 + -6 = 7.211102551 Reorder the terms: -6 + a2 = 7.211102551 Solving -6 + a2 = 7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a2 = 7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + a2 = 7.211102551 + 6 a2 = 7.211102551 + 6 Combine like terms: 7.211102551 + 6 = 13.211102551 a2 = 13.211102551 Simplifying a2 = 13.211102551 Take the square root of each side: a = {-3.634708042, 3.634708042}Subproblem 2
a2 + -6 = -7.211102551 Simplifying a2 + -6 = -7.211102551 Reorder the terms: -6 + a2 = -7.211102551 Solving -6 + a2 = -7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a2 = -7.211102551 + 6 Combine like terms: -6 + 6 = 0 0 + a2 = -7.211102551 + 6 a2 = -7.211102551 + 6 Combine like terms: -7.211102551 + 6 = -1.211102551 a2 = -1.211102551 Simplifying a2 = -1.211102551 Reorder the terms: 1.211102551 + a2 = -1.211102551 + 1.211102551 Combine like terms: -1.211102551 + 1.211102551 = 0.000000000 1.211102551 + 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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