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Simplifying n2 + n + -2400 = 0 Reorder the terms: -2400 + n + n2 = 0 Solving -2400 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2400' to each side of the equation. -2400 + n + 2400 + n2 = 0 + 2400 Reorder the terms: -2400 + 2400 + n + n2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + n + n2 = 0 + 2400 n + n2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 n + n2 = 2400 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 = 2400 + 0.25 Reorder the terms: 0.25 + n + n2 = 2400 + 0.25 Combine like terms: 2400 + 0.25 = 2400.25 0.25 + n + n2 = 2400.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 2400.25 Calculate the square root of the right side: 48.992346341 Break this problem into two subproblems by setting (n + 0.5) equal to 48.992346341 and -48.992346341.Subproblem 1
n + 0.5 = 48.992346341 Simplifying n + 0.5 = 48.992346341 Reorder the terms: 0.5 + n = 48.992346341 Solving 0.5 + n = 48.992346341 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 = 48.992346341 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 48.992346341 + -0.5 n = 48.992346341 + -0.5 Combine like terms: 48.992346341 + -0.5 = 48.492346341 n = 48.492346341 Simplifying n = 48.492346341Subproblem 2
n + 0.5 = -48.992346341 Simplifying n + 0.5 = -48.992346341 Reorder the terms: 0.5 + n = -48.992346341 Solving 0.5 + n = -48.992346341 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 = -48.992346341 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -48.992346341 + -0.5 n = -48.992346341 + -0.5 Combine like terms: -48.992346341 + -0.5 = -49.492346341 n = -49.492346341 Simplifying n = -49.492346341Solution
The solution to the problem is based on the solutions from the subproblems. n = {48.492346341, -49.492346341}
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