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Simplifying n2 + n + -18000 = 0 Reorder the terms: -18000 + n + n2 = 0 Solving -18000 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '18000' to each side of the equation. -18000 + n + 18000 + n2 = 0 + 18000 Reorder the terms: -18000 + 18000 + n + n2 = 0 + 18000 Combine like terms: -18000 + 18000 = 0 0 + n + n2 = 0 + 18000 n + n2 = 0 + 18000 Combine like terms: 0 + 18000 = 18000 n + n2 = 18000 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 18000 + 0.25 Reorder the terms: 0.25 + n + n2 = 18000 + 0.25 Combine like terms: 18000 + 0.25 = 18000.25 0.25 + n + n2 = 18000.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 18000.25 Calculate the square root of the right side: 134.165010342 Break this problem into two subproblems by setting (n + 0.5) equal to 134.165010342 and -134.165010342.Subproblem 1
n + 0.5 = 134.165010342 Simplifying n + 0.5 = 134.165010342 Reorder the terms: 0.5 + n = 134.165010342 Solving 0.5 + n = 134.165010342 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 134.165010342 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 134.165010342 + -0.5 n = 134.165010342 + -0.5 Combine like terms: 134.165010342 + -0.5 = 133.665010342 n = 133.665010342 Simplifying n = 133.665010342Subproblem 2
n + 0.5 = -134.165010342 Simplifying n + 0.5 = -134.165010342 Reorder the terms: 0.5 + n = -134.165010342 Solving 0.5 + n = -134.165010342 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -134.165010342 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -134.165010342 + -0.5 n = -134.165010342 + -0.5 Combine like terms: -134.165010342 + -0.5 = -134.665010342 n = -134.665010342 Simplifying n = -134.665010342Solution
The solution to the problem is based on the solutions from the subproblems. n = {133.665010342, -134.665010342}
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