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Simplifying z4 + 8z2 + 9 = 0 Reorder the terms: 9 + 8z2 + z4 = 0 Solving 9 + 8z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8z2 + -9 + z4 = 0 + -9 Reorder the terms: 9 + -9 + 8z2 + z4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8z2 + z4 = 0 + -9 8z2 + z4 = 0 + -9 Combine like terms: 0 + -9 = -9 8z2 + z4 = -9 The z term is 8z2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8z2 + 16 + z4 = -9 + 16 Reorder the terms: 16 + 8z2 + z4 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8z2 + z4 = 7 Factor a perfect square on the left side: (z2 + 4)(z2 + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (z2 + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
z2 + 4 = 2.645751311 Simplifying z2 + 4 = 2.645751311 Reorder the terms: 4 + z2 = 2.645751311 Solving 4 + z2 = 2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z2 = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + z2 = 2.645751311 + -4 z2 = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 z2 = -1.354248689 Simplifying z2 = -1.354248689 Reorder the terms: 1.354248689 + z2 = -1.354248689 + 1.354248689 Combine like terms: -1.354248689 + 1.354248689 = 0.000000000 1.354248689 + z2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
z2 + 4 = -2.645751311 Simplifying z2 + 4 = -2.645751311 Reorder the terms: 4 + z2 = -2.645751311 Solving 4 + z2 = -2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z2 = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + z2 = -2.645751311 + -4 z2 = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 z2 = -6.645751311 Simplifying z2 = -6.645751311 Reorder the terms: 6.645751311 + z2 = -6.645751311 + 6.645751311 Combine like terms: -6.645751311 + 6.645751311 = 0.000000000 6.645751311 + z2 = 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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