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Simplifying n2 + n + -340 = 0 Reorder the terms: -340 + n + n2 = 0 Solving -340 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + n + 340 + n2 = 0 + 340 Reorder the terms: -340 + 340 + n + n2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + n + n2 = 0 + 340 n + n2 = 0 + 340 Combine like terms: 0 + 340 = 340 n + n2 = 340 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 = 340 + 0.25 Reorder the terms: 0.25 + n + n2 = 340 + 0.25 Combine like terms: 340 + 0.25 = 340.25 0.25 + n + n2 = 340.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 340.25 Calculate the square root of the right side: 18.445866746 Break this problem into two subproblems by setting (n + 0.5) equal to 18.445866746 and -18.445866746.Subproblem 1
n + 0.5 = 18.445866746 Simplifying n + 0.5 = 18.445866746 Reorder the terms: 0.5 + n = 18.445866746 Solving 0.5 + n = 18.445866746 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 = 18.445866746 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 18.445866746 + -0.5 n = 18.445866746 + -0.5 Combine like terms: 18.445866746 + -0.5 = 17.945866746 n = 17.945866746 Simplifying n = 17.945866746Subproblem 2
n + 0.5 = -18.445866746 Simplifying n + 0.5 = -18.445866746 Reorder the terms: 0.5 + n = -18.445866746 Solving 0.5 + n = -18.445866746 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 = -18.445866746 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -18.445866746 + -0.5 n = -18.445866746 + -0.5 Combine like terms: -18.445866746 + -0.5 = -18.945866746 n = -18.945866746 Simplifying n = -18.945866746Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.945866746, -18.945866746}
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