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Simplifying z2 + -11z = 30 Reorder the terms: -11z + z2 = 30 Solving -11z + z2 = 30 Solving for variable 'z'. Reorder the terms: -30 + -11z + z2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -11z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -11z + 30 + z2 = 0 + 30 Reorder the terms: -30 + 30 + -11z + z2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -11z + z2 = 0 + 30 -11z + z2 = 0 + 30 Combine like terms: 0 + 30 = 30 -11z + z2 = 30 The z term is -11z. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11z + 30.25 + z2 = 30 + 30.25 Reorder the terms: 30.25 + -11z + z2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + -11z + z2 = 60.25 Factor a perfect square on the left side: (z + -5.5)(z + -5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (z + -5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
z + -5.5 = 7.762087348 Simplifying z + -5.5 = 7.762087348 Reorder the terms: -5.5 + z = 7.762087348 Solving -5.5 + z = 7.762087348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + z = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = 7.762087348 + 5.5 z = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 z = 13.262087348 Simplifying z = 13.262087348Subproblem 2
z + -5.5 = -7.762087348 Simplifying z + -5.5 = -7.762087348 Reorder the terms: -5.5 + z = -7.762087348 Solving -5.5 + z = -7.762087348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + z = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = -7.762087348 + 5.5 z = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 z = -2.262087348 Simplifying z = -2.262087348Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.262087348, -2.262087348}
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