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Simplifying z6 + -2z3 + -4 = 0 Reorder the terms: -4 + -2z3 + z6 = 0 Solving -4 + -2z3 + z6 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2z3 + 4 + z6 = 0 + 4 Reorder the terms: -4 + 4 + -2z3 + z6 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2z3 + z6 = 0 + 4 -2z3 + z6 = 0 + 4 Combine like terms: 0 + 4 = 4 -2z3 + z6 = 4 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 = 4 + 1 Reorder the terms: 1 + -2z3 + z6 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2z3 + z6 = 5 Factor a perfect square on the left side: (z3 + -1)(z3 + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (z3 + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
z3 + -1 = 2.236067978 Simplifying z3 + -1 = 2.236067978 Reorder the terms: -1 + z3 = 2.236067978 Solving -1 + z3 = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = 2.236067978 + 1 z3 = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 z3 = 3.236067978 Simplifying z3 = 3.236067978 Reorder the terms: -3.236067978 + z3 = 3.236067978 + -3.236067978 Combine like terms: 3.236067978 + -3.236067978 = 0.000000000 -3.236067978 + 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 = -2.236067978 Simplifying z3 + -1 = -2.236067978 Reorder the terms: -1 + z3 = -2.236067978 Solving -1 + z3 = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + z3 = -2.236067978 + 1 z3 = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 z3 = -1.236067978 Simplifying z3 = -1.236067978 Reorder the terms: 1.236067978 + z3 = -1.236067978 + 1.236067978 Combine like terms: -1.236067978 + 1.236067978 = 0.000000000 1.236067978 + 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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