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Simplifying n2 + n = 39 Reorder the terms: n + n2 = 39 Solving n + n2 = 39 Solving for variable 'n'. Reorder the terms: -39 + n + n2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + n + 39 + n2 = 0 + 39 Reorder the terms: -39 + 39 + n + n2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + n + n2 = 0 + 39 n + n2 = 0 + 39 Combine like terms: 0 + 39 = 39 n + n2 = 39 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 = 39 + 0.25 Reorder the terms: 0.25 + n + n2 = 39 + 0.25 Combine like terms: 39 + 0.25 = 39.25 0.25 + n + n2 = 39.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (n + 0.5) equal to 6.264982043 and -6.264982043.Subproblem 1
n + 0.5 = 6.264982043 Simplifying n + 0.5 = 6.264982043 Reorder the terms: 0.5 + n = 6.264982043 Solving 0.5 + n = 6.264982043 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 = 6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 6.264982043 + -0.5 n = 6.264982043 + -0.5 Combine like terms: 6.264982043 + -0.5 = 5.764982043 n = 5.764982043 Simplifying n = 5.764982043Subproblem 2
n + 0.5 = -6.264982043 Simplifying n + 0.5 = -6.264982043 Reorder the terms: 0.5 + n = -6.264982043 Solving 0.5 + n = -6.264982043 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 = -6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -6.264982043 + -0.5 n = -6.264982043 + -0.5 Combine like terms: -6.264982043 + -0.5 = -6.764982043 n = -6.764982043 Simplifying n = -6.764982043Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.764982043, -6.764982043}
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