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Simplifying 2n2 + -22n = 60 Reorder the terms: -22n + 2n2 = 60 Solving -22n + 2n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + -22n + 2n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -22n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -11n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -11n + n2)' equal to zero and attempt to solve: Simplifying -30 + -11n + n2 = 0 Solving -30 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -11n + 30 + n2 = 0 + 30 Reorder the terms: -30 + 30 + -11n + n2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -11n + n2 = 0 + 30 -11n + n2 = 0 + 30 Combine like terms: 0 + 30 = 30 -11n + n2 = 30 The n term is -11n. 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. -11n + 30.25 + n2 = 30 + 30.25 Reorder the terms: 30.25 + -11n + n2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + -11n + n2 = 60.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (n + -5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
n + -5.5 = 7.762087348 Simplifying n + -5.5 = 7.762087348 Reorder the terms: -5.5 + n = 7.762087348 Solving -5.5 + n = 7.762087348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 7.762087348 + 5.5 n = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 n = 13.262087348 Simplifying n = 13.262087348Subproblem 2
n + -5.5 = -7.762087348 Simplifying n + -5.5 = -7.762087348 Reorder the terms: -5.5 + n = -7.762087348 Solving -5.5 + n = -7.762087348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -7.762087348 + 5.5 n = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 n = -2.262087348 Simplifying n = -2.262087348Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.262087348, -2.262087348}Solution
n = {13.262087348, -2.262087348}
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