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Simplifying z * z + -1z = 44 Multiply z * z z2 + -1z = 44 Reorder the terms: -1z + z2 = 44 Solving -1z + z2 = 44 Solving for variable 'z'. Reorder the terms: -44 + -1z + z2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -1z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -1z + 44 + z2 = 0 + 44 Reorder the terms: -44 + 44 + -1z + z2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -1z + z2 = 0 + 44 -1z + z2 = 0 + 44 Combine like terms: 0 + 44 = 44 -1z + z2 = 44 The z term is -1z. 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. -1z + 0.25 + z2 = 44 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + -1z + z2 = 44.25 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (z + -0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
z + -0.5 = 6.652067348 Simplifying z + -0.5 = 6.652067348 Reorder the terms: -0.5 + z = 6.652067348 Solving -0.5 + z = 6.652067348 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 + z = 6.652067348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 6.652067348 + 0.5 z = 6.652067348 + 0.5 Combine like terms: 6.652067348 + 0.5 = 7.152067348 z = 7.152067348 Simplifying z = 7.152067348Subproblem 2
z + -0.5 = -6.652067348 Simplifying z + -0.5 = -6.652067348 Reorder the terms: -0.5 + z = -6.652067348 Solving -0.5 + z = -6.652067348 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 + z = -6.652067348 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -6.652067348 + 0.5 z = -6.652067348 + 0.5 Combine like terms: -6.652067348 + 0.5 = -6.152067348 z = -6.152067348 Simplifying z = -6.152067348Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.152067348, -6.152067348}
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