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Simplifying (n2) + -18n = 81 n2 + -18n = 81 Reorder the terms: -18n + n2 = 81 Solving -18n + n2 = 81 Solving for variable 'n'. Reorder the terms: -81 + -18n + n2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -18n + 81 + n2 = 0 + 81 Reorder the terms: -81 + 81 + -18n + n2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -18n + n2 = 0 + 81 -18n + n2 = 0 + 81 Combine like terms: 0 + 81 = 81 -18n + n2 = 81 The n term is -18n. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18n + 81 + n2 = 81 + 81 Reorder the terms: 81 + -18n + n2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + -18n + n2 = 162 Factor a perfect square on the left side: (n + -9)(n + -9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (n + -9) equal to 12.727922061 and -12.727922061.Subproblem 1
n + -9 = 12.727922061 Simplifying n + -9 = 12.727922061 Reorder the terms: -9 + n = 12.727922061 Solving -9 + n = 12.727922061 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = 12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + n = 12.727922061 + 9 n = 12.727922061 + 9 Combine like terms: 12.727922061 + 9 = 21.727922061 n = 21.727922061 Simplifying n = 21.727922061Subproblem 2
n + -9 = -12.727922061 Simplifying n + -9 = -12.727922061 Reorder the terms: -9 + n = -12.727922061 Solving -9 + n = -12.727922061 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = -12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + n = -12.727922061 + 9 n = -12.727922061 + 9 Combine like terms: -12.727922061 + 9 = -3.727922061 n = -3.727922061 Simplifying n = -3.727922061Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.727922061, -3.727922061}
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