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Simplifying n2 + -5n + -82 = 0 Reorder the terms: -82 + -5n + n2 = 0 Solving -82 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -5n + 82 + n2 = 0 + 82 Reorder the terms: -82 + 82 + -5n + n2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -5n + n2 = 0 + 82 -5n + n2 = 0 + 82 Combine like terms: 0 + 82 = 82 -5n + n2 = 82 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 = 82 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 82 + 6.25 Combine like terms: 82 + 6.25 = 88.25 6.25 + -5n + n2 = 88.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (n + -2.5) equal to 9.394147114 and -9.394147114.Subproblem 1
n + -2.5 = 9.394147114 Simplifying n + -2.5 = 9.394147114 Reorder the terms: -2.5 + n = 9.394147114 Solving -2.5 + n = 9.394147114 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 = 9.394147114 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 9.394147114 + 2.5 n = 9.394147114 + 2.5 Combine like terms: 9.394147114 + 2.5 = 11.894147114 n = 11.894147114 Simplifying n = 11.894147114Subproblem 2
n + -2.5 = -9.394147114 Simplifying n + -2.5 = -9.394147114 Reorder the terms: -2.5 + n = -9.394147114 Solving -2.5 + n = -9.394147114 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 = -9.394147114 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -9.394147114 + 2.5 n = -9.394147114 + 2.5 Combine like terms: -9.394147114 + 2.5 = -6.894147114 n = -6.894147114 Simplifying n = -6.894147114Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.894147114, -6.894147114}
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