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Simplifying z7 + -2z4 + -2z = 0 Reorder the terms: -2z + -2z4 + z7 = 0 Solving -2z + -2z4 + z7 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-2 + -2z3 + z6) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-2 + -2z3 + z6)' equal to zero and attempt to solve: Simplifying -2 + -2z3 + z6 = 0 Solving -2 + -2z3 + z6 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2z3 + 2 + z6 = 0 + 2 Reorder the terms: -2 + 2 + -2z3 + z6 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2z3 + z6 = 0 + 2 -2z3 + z6 = 0 + 2 Combine like terms: 0 + 2 = 2 -2z3 + z6 = 2 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 = 2 + 1 Reorder the terms: 1 + -2z3 + z6 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2z3 + z6 = 3 Factor a perfect square on the left side: (z3 + -1)(z3 + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (z3 + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
z3 + -1 = 1.732050808 Simplifying z3 + -1 = 1.732050808 Reorder the terms: -1 + z3 = 1.732050808 Solving -1 + z3 = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = 1.732050808 + 1 z3 = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 z3 = 2.732050808 Simplifying z3 = 2.732050808 Reorder the terms: -2.732050808 + z3 = 2.732050808 + -2.732050808 Combine like terms: 2.732050808 + -2.732050808 = 0.000000000 -2.732050808 + 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 = -1.732050808 Simplifying z3 + -1 = -1.732050808 Reorder the terms: -1 + z3 = -1.732050808 Solving -1 + z3 = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = -1.732050808 + 1 z3 = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 z3 = -0.732050808 Simplifying z3 = -0.732050808 Reorder the terms: 0.732050808 + z3 = -0.732050808 + 0.732050808 Combine like terms: -0.732050808 + 0.732050808 = 0.000000000 0.732050808 + 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. This subproblem is being ignored because a solution could not be determined.Solution
z = {0}
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