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Simplifying n2 + n + -6 = 182 Reorder the terms: -6 + n + n2 = 182 Solving -6 + n + n2 = 182 Solving for variable 'n'. Reorder the terms: -6 + -182 + n + n2 = 182 + -182 Combine like terms: -6 + -182 = -188 -188 + n + n2 = 182 + -182 Combine like terms: 182 + -182 = 0 -188 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + n + 188 + n2 = 0 + 188 Reorder the terms: -188 + 188 + n + n2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + n + n2 = 0 + 188 n + n2 = 0 + 188 Combine like terms: 0 + 188 = 188 n + n2 = 188 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 = 188 + 0.25 Reorder the terms: 0.25 + n + n2 = 188 + 0.25 Combine like terms: 188 + 0.25 = 188.25 0.25 + n + n2 = 188.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 188.25 Calculate the square root of the right side: 13.720422734 Break this problem into two subproblems by setting (n + 0.5) equal to 13.720422734 and -13.720422734.Subproblem 1
n + 0.5 = 13.720422734 Simplifying n + 0.5 = 13.720422734 Reorder the terms: 0.5 + n = 13.720422734 Solving 0.5 + n = 13.720422734 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 = 13.720422734 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 13.720422734 + -0.5 n = 13.720422734 + -0.5 Combine like terms: 13.720422734 + -0.5 = 13.220422734 n = 13.220422734 Simplifying n = 13.220422734Subproblem 2
n + 0.5 = -13.720422734 Simplifying n + 0.5 = -13.720422734 Reorder the terms: 0.5 + n = -13.720422734 Solving 0.5 + n = -13.720422734 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 = -13.720422734 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -13.720422734 + -0.5 n = -13.720422734 + -0.5 Combine like terms: -13.720422734 + -0.5 = -14.220422734 n = -14.220422734 Simplifying n = -14.220422734Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.220422734, -14.220422734}
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