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Simplifying n2 + -5n + -60 = 0 Reorder the terms: -60 + -5n + n2 = 0 Solving -60 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -5n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + -5n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -5n + n2 = 0 + 60 -5n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 -5n + n2 = 60 The n term is -5n. 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. -5n + 6.25 + n2 = 60 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 60 + 6.25 Combine like terms: 60 + 6.25 = 66.25 6.25 + -5n + n2 = 66.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (n + -2.5) equal to 8.139410298 and -8.139410298.Subproblem 1
n + -2.5 = 8.139410298 Simplifying n + -2.5 = 8.139410298 Reorder the terms: -2.5 + n = 8.139410298 Solving -2.5 + n = 8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 8.139410298 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 8.139410298 + 2.5 n = 8.139410298 + 2.5 Combine like terms: 8.139410298 + 2.5 = 10.639410298 n = 10.639410298 Simplifying n = 10.639410298Subproblem 2
n + -2.5 = -8.139410298 Simplifying n + -2.5 = -8.139410298 Reorder the terms: -2.5 + n = -8.139410298 Solving -2.5 + n = -8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -8.139410298 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -8.139410298 + 2.5 n = -8.139410298 + 2.5 Combine like terms: -8.139410298 + 2.5 = -5.639410298 n = -5.639410298 Simplifying n = -5.639410298Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.639410298, -5.639410298}
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