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Simplifying n2 + n + -1440 = 0 Reorder the terms: -1440 + n + n2 = 0 Solving -1440 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1440' to each side of the equation. -1440 + n + 1440 + n2 = 0 + 1440 Reorder the terms: -1440 + 1440 + n + n2 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + n + n2 = 0 + 1440 n + n2 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 n + n2 = 1440 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 = 1440 + 0.25 Reorder the terms: 0.25 + n + n2 = 1440 + 0.25 Combine like terms: 1440 + 0.25 = 1440.25 0.25 + n + n2 = 1440.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1440.25 Calculate the square root of the right side: 37.950625818 Break this problem into two subproblems by setting (n + 0.5) equal to 37.950625818 and -37.950625818.Subproblem 1
n + 0.5 = 37.950625818 Simplifying n + 0.5 = 37.950625818 Reorder the terms: 0.5 + n = 37.950625818 Solving 0.5 + n = 37.950625818 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 = 37.950625818 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 37.950625818 + -0.5 n = 37.950625818 + -0.5 Combine like terms: 37.950625818 + -0.5 = 37.450625818 n = 37.450625818 Simplifying n = 37.450625818Subproblem 2
n + 0.5 = -37.950625818 Simplifying n + 0.5 = -37.950625818 Reorder the terms: 0.5 + n = -37.950625818 Solving 0.5 + n = -37.950625818 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 = -37.950625818 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -37.950625818 + -0.5 n = -37.950625818 + -0.5 Combine like terms: -37.950625818 + -0.5 = -38.450625818 n = -38.450625818 Simplifying n = -38.450625818Solution
The solution to the problem is based on the solutions from the subproblems. n = {37.450625818, -38.450625818}
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