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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 = 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.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 = -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. The solution to this equation could not be determined.
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