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Simplifying n2 + n + -2956 = 0 Reorder the terms: -2956 + n + n2 = 0 Solving -2956 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2956' to each side of the equation. -2956 + n + 2956 + n2 = 0 + 2956 Reorder the terms: -2956 + 2956 + n + n2 = 0 + 2956 Combine like terms: -2956 + 2956 = 0 0 + n + n2 = 0 + 2956 n + n2 = 0 + 2956 Combine like terms: 0 + 2956 = 2956 n + n2 = 2956 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 = 2956 + 0.25 Reorder the terms: 0.25 + n + n2 = 2956 + 0.25 Combine like terms: 2956 + 0.25 = 2956.25 0.25 + n + n2 = 2956.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 2956.25 Calculate the square root of the right side: 54.371407927 Break this problem into two subproblems by setting (n + 0.5) equal to 54.371407927 and -54.371407927.Subproblem 1
n + 0.5 = 54.371407927 Simplifying n + 0.5 = 54.371407927 Reorder the terms: 0.5 + n = 54.371407927 Solving 0.5 + n = 54.371407927 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 = 54.371407927 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 54.371407927 + -0.5 n = 54.371407927 + -0.5 Combine like terms: 54.371407927 + -0.5 = 53.871407927 n = 53.871407927 Simplifying n = 53.871407927Subproblem 2
n + 0.5 = -54.371407927 Simplifying n + 0.5 = -54.371407927 Reorder the terms: 0.5 + n = -54.371407927 Solving 0.5 + n = -54.371407927 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 = -54.371407927 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -54.371407927 + -0.5 n = -54.371407927 + -0.5 Combine like terms: -54.371407927 + -0.5 = -54.871407927 n = -54.871407927 Simplifying n = -54.871407927Solution
The solution to the problem is based on the solutions from the subproblems. n = {53.871407927, -54.871407927}
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