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Simplifying n2 + 18n + -44 = 0 Reorder the terms: -44 + 18n + n2 = 0 Solving -44 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 18n + 44 + n2 = 0 + 44 Reorder the terms: -44 + 44 + 18n + n2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 18n + n2 = 0 + 44 18n + n2 = 0 + 44 Combine like terms: 0 + 44 = 44 18n + n2 = 44 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 = 44 + 81 Reorder the terms: 81 + 18n + n2 = 44 + 81 Combine like terms: 44 + 81 = 125 81 + 18n + n2 = 125 Factor a perfect square on the left side: (n + 9)(n + 9) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (n + 9) equal to 11.180339887 and -11.180339887.Subproblem 1
n + 9 = 11.180339887 Simplifying n + 9 = 11.180339887 Reorder the terms: 9 + n = 11.180339887 Solving 9 + n = 11.180339887 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 = 11.180339887 + -9 Combine like terms: 9 + -9 = 0 0 + n = 11.180339887 + -9 n = 11.180339887 + -9 Combine like terms: 11.180339887 + -9 = 2.180339887 n = 2.180339887 Simplifying n = 2.180339887Subproblem 2
n + 9 = -11.180339887 Simplifying n + 9 = -11.180339887 Reorder the terms: 9 + n = -11.180339887 Solving 9 + n = -11.180339887 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 = -11.180339887 + -9 Combine like terms: 9 + -9 = 0 0 + n = -11.180339887 + -9 n = -11.180339887 + -9 Combine like terms: -11.180339887 + -9 = -20.180339887 n = -20.180339887 Simplifying n = -20.180339887Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.180339887, -20.180339887}
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