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Simplifying z4 + z2 = 15 Reorder the terms: z2 + z4 = 15 Solving z2 + z4 = 15 Solving for variable 'z'. Reorder the terms: -15 + z2 + z4 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + z2 + z4 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + z2 + 15 + z4 = 0 + 15 Reorder the terms: -15 + 15 + z2 + z4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + z2 + z4 = 0 + 15 z2 + z4 = 0 + 15 Combine like terms: 0 + 15 = 15 z2 + z4 = 15 The z term is z2. 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. z2 + 0.25 + z4 = 15 + 0.25 Reorder the terms: 0.25 + z2 + z4 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + z2 + z4 = 15.25 Factor a perfect square on the left side: (z2 + 0.5)(z2 + 0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (z2 + 0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
z2 + 0.5 = 3.905124838 Simplifying z2 + 0.5 = 3.905124838 Reorder the terms: 0.5 + z2 = 3.905124838 Solving 0.5 + z2 = 3.905124838 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 = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z2 = 3.905124838 + -0.5 z2 = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 z2 = 3.405124838 Simplifying z2 = 3.405124838 Take the square root of each side: z = {-1.845298035, 1.845298035}Subproblem 2
z2 + 0.5 = -3.905124838 Simplifying z2 + 0.5 = -3.905124838 Reorder the terms: 0.5 + z2 = -3.905124838 Solving 0.5 + z2 = -3.905124838 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 = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z2 = -3.905124838 + -0.5 z2 = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 z2 = -4.405124838 Simplifying z2 = -4.405124838 Reorder the terms: 4.405124838 + z2 = -4.405124838 + 4.405124838 Combine like terms: -4.405124838 + 4.405124838 = 0.000000000 4.405124838 + 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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