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Simplifying n2 + -81 = -5n Reorder the terms: -81 + n2 = -5n Solving -81 + n2 = -5n Solving for variable 'n'. Reorder the terms: -81 + 5n + n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -81 + 5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 5n + 81 + n2 = 0 + 81 Reorder the terms: -81 + 81 + 5n + n2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 5n + n2 = 0 + 81 5n + n2 = 0 + 81 Combine like terms: 0 + 81 = 81 5n + n2 = 81 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 = 81 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 81 + 6.25 Combine like terms: 81 + 6.25 = 87.25 6.25 + 5n + n2 = 87.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (n + 2.5) equal to 9.340770846 and -9.340770846.Subproblem 1
n + 2.5 = 9.340770846 Simplifying n + 2.5 = 9.340770846 Reorder the terms: 2.5 + n = 9.340770846 Solving 2.5 + n = 9.340770846 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 = 9.340770846 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 9.340770846 + -2.5 n = 9.340770846 + -2.5 Combine like terms: 9.340770846 + -2.5 = 6.840770846 n = 6.840770846 Simplifying n = 6.840770846Subproblem 2
n + 2.5 = -9.340770846 Simplifying n + 2.5 = -9.340770846 Reorder the terms: 2.5 + n = -9.340770846 Solving 2.5 + n = -9.340770846 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 = -9.340770846 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -9.340770846 + -2.5 n = -9.340770846 + -2.5 Combine like terms: -9.340770846 + -2.5 = -11.840770846 n = -11.840770846 Simplifying n = -11.840770846Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.840770846, -11.840770846}
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