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Simplifying 2z2 + -10z = 12110 Reorder the terms: -10z + 2z2 = 12110 Solving -10z + 2z2 = 12110 Solving for variable 'z'. Reorder the terms: -12110 + -10z + 2z2 = 12110 + -12110 Combine like terms: 12110 + -12110 = 0 -12110 + -10z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6055 + -5z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6055 + -5z + z2)' equal to zero and attempt to solve: Simplifying -6055 + -5z + z2 = 0 Solving -6055 + -5z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '6055' to each side of the equation. -6055 + -5z + 6055 + z2 = 0 + 6055 Reorder the terms: -6055 + 6055 + -5z + z2 = 0 + 6055 Combine like terms: -6055 + 6055 = 0 0 + -5z + z2 = 0 + 6055 -5z + z2 = 0 + 6055 Combine like terms: 0 + 6055 = 6055 -5z + z2 = 6055 The z term is -5z. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5z + 6.25 + z2 = 6055 + 6.25 Reorder the terms: 6.25 + -5z + z2 = 6055 + 6.25 Combine like terms: 6055 + 6.25 = 6061.25 6.25 + -5z + z2 = 6061.25 Factor a perfect square on the left side: (z + -2.5)(z + -2.5) = 6061.25 Calculate the square root of the right side: 77.854030082 Break this problem into two subproblems by setting (z + -2.5) equal to 77.854030082 and -77.854030082.Subproblem 1
z + -2.5 = 77.854030082 Simplifying z + -2.5 = 77.854030082 Reorder the terms: -2.5 + z = 77.854030082 Solving -2.5 + z = 77.854030082 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = 77.854030082 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = 77.854030082 + 2.5 z = 77.854030082 + 2.5 Combine like terms: 77.854030082 + 2.5 = 80.354030082 z = 80.354030082 Simplifying z = 80.354030082Subproblem 2
z + -2.5 = -77.854030082 Simplifying z + -2.5 = -77.854030082 Reorder the terms: -2.5 + z = -77.854030082 Solving -2.5 + z = -77.854030082 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = -77.854030082 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = -77.854030082 + 2.5 z = -77.854030082 + 2.5 Combine like terms: -77.854030082 + 2.5 = -75.354030082 z = -75.354030082 Simplifying z = -75.354030082Solution
The solution to the problem is based on the solutions from the subproblems. z = {80.354030082, -75.354030082}Solution
z = {80.354030082, -75.354030082}
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