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Simplifying z6 + -2z3 + -1 = 0 Reorder the terms: -1 + -2z3 + z6 = 0 Solving -1 + -2z3 + z6 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -2z3 + 1 + z6 = 0 + 1 Reorder the terms: -1 + 1 + -2z3 + z6 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z3 + z6 = 0 + 1 -2z3 + z6 = 0 + 1 Combine like terms: 0 + 1 = 1 -2z3 + z6 = 1 The z term is -2z3. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2z3 + 1 + z6 = 1 + 1 Reorder the terms: 1 + -2z3 + z6 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2z3 + z6 = 2 Factor a perfect square on the left side: (z3 + -1)(z3 + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (z3 + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
z3 + -1 = 1.414213562 Simplifying z3 + -1 = 1.414213562 Reorder the terms: -1 + z3 = 1.414213562 Solving -1 + z3 = 1.414213562 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 + z3 = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = 1.414213562 + 1 z3 = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 z3 = 2.414213562 Simplifying z3 = 2.414213562 Reorder the terms: -2.414213562 + z3 = 2.414213562 + -2.414213562 Combine like terms: 2.414213562 + -2.414213562 = 0.000000000 -2.414213562 + z3 = 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
z3 + -1 = -1.414213562 Simplifying z3 + -1 = -1.414213562 Reorder the terms: -1 + z3 = -1.414213562 Solving -1 + z3 = -1.414213562 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 + z3 = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = -1.414213562 + 1 z3 = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 z3 = -0.414213562 Simplifying z3 = -0.414213562 Reorder the terms: 0.414213562 + z3 = -0.414213562 + 0.414213562 Combine like terms: -0.414213562 + 0.414213562 = 0.000000000 0.414213562 + z3 = 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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