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Simplifying z4 + -1z2 + -3 = 0 Reorder the terms: -3 + -1z2 + z4 = 0 Solving -3 + -1z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1z2 + 3 + z4 = 0 + 3 Reorder the terms: -3 + 3 + -1z2 + z4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z2 + z4 = 0 + 3 -1z2 + z4 = 0 + 3 Combine like terms: 0 + 3 = 3 -1z2 + z4 = 3 The z term is -1z2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z2 + 0.25 + z4 = 3 + 0.25 Reorder the terms: 0.25 + -1z2 + z4 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1z2 + z4 = 3.25 Factor a perfect square on the left side: (z2 + -0.5)(z2 + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (z2 + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
z2 + -0.5 = 1.802775638 Simplifying z2 + -0.5 = 1.802775638 Reorder the terms: -0.5 + z2 = 1.802775638 Solving -0.5 + z2 = 1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z2 = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z2 = 1.802775638 + 0.5 z2 = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 z2 = 2.302775638 Simplifying z2 = 2.302775638 Take the square root of each side: z = {-1.517489914, 1.517489914}Subproblem 2
z2 + -0.5 = -1.802775638 Simplifying z2 + -0.5 = -1.802775638 Reorder the terms: -0.5 + z2 = -1.802775638 Solving -0.5 + z2 = -1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z2 = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z2 = -1.802775638 + 0.5 z2 = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 z2 = -1.302775638 Simplifying z2 = -1.302775638 Reorder the terms: 1.302775638 + z2 = -1.302775638 + 1.302775638 Combine like terms: -1.302775638 + 1.302775638 = 0.000000000 1.302775638 + 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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