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Simplifying 5z4 + 10z2 + 1 = 0 Reorder the terms: 1 + 10z2 + 5z4 = 0 Solving 1 + 10z2 + 5z4 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2z2 + z4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2z2 + -0.2 + z4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2z2 + z4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2z2 + z4 = 0 + -0.2 2z2 + z4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2z2 + z4 = -0.2 The z term is 2z2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z2 + 1 + z4 = -0.2 + 1 Reorder the terms: 1 + 2z2 + z4 = -0.2 + 1 Combine like terms: -0.2 + 1 = 0.8 1 + 2z2 + z4 = 0.8 Factor a perfect square on the left side: (z2 + 1)(z2 + 1) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (z2 + 1) equal to 0.894427191 and -0.894427191.Subproblem 1
z2 + 1 = 0.894427191 Simplifying z2 + 1 = 0.894427191 Reorder the terms: 1 + z2 = 0.894427191 Solving 1 + z2 = 0.894427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z2 = 0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + z2 = 0.894427191 + -1 z2 = 0.894427191 + -1 Combine like terms: 0.894427191 + -1 = -0.105572809 z2 = -0.105572809 Simplifying z2 = -0.105572809 Reorder the terms: 0.105572809 + z2 = -0.105572809 + 0.105572809 Combine like terms: -0.105572809 + 0.105572809 = 0.000000000 0.105572809 + 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 + 1 = -0.894427191 Simplifying z2 + 1 = -0.894427191 Reorder the terms: 1 + z2 = -0.894427191 Solving 1 + z2 = -0.894427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z2 = -0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + z2 = -0.894427191 + -1 z2 = -0.894427191 + -1 Combine like terms: -0.894427191 + -1 = -1.894427191 z2 = -1.894427191 Simplifying z2 = -1.894427191 Reorder the terms: 1.894427191 + z2 = -1.894427191 + 1.894427191 Combine like terms: -1.894427191 + 1.894427191 = 0.000000000 1.894427191 + 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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