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Simplifying n2 + -2n + -1 = 38.5 Reorder the terms: -1 + -2n + n2 = 38.5 Solving -1 + -2n + n2 = 38.5 Solving for variable 'n'. Reorder the terms: -1 + -38.5 + -2n + n2 = 38.5 + -38.5 Combine like terms: -1 + -38.5 = -39.5 -39.5 + -2n + n2 = 38.5 + -38.5 Combine like terms: 38.5 + -38.5 = 0.0 -39.5 + -2n + n2 = 0.0 Begin completing the square. Move the constant term to the right: Add '39.5' to each side of the equation. -39.5 + -2n + 39.5 + n2 = 0.0 + 39.5 Reorder the terms: -39.5 + 39.5 + -2n + n2 = 0.0 + 39.5 Combine like terms: -39.5 + 39.5 = 0.0 0.0 + -2n + n2 = 0.0 + 39.5 -2n + n2 = 0.0 + 39.5 Combine like terms: 0.0 + 39.5 = 39.5 -2n + n2 = 39.5 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 39.5 + 1 Reorder the terms: 1 + -2n + n2 = 39.5 + 1 Combine like terms: 39.5 + 1 = 40.5 1 + -2n + n2 = 40.5 Factor a perfect square on the left side: (n + -1)(n + -1) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (n + -1) equal to 6.363961031 and -6.363961031.Subproblem 1
n + -1 = 6.363961031 Simplifying n + -1 = 6.363961031 Reorder the terms: -1 + n = 6.363961031 Solving -1 + n = 6.363961031 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 6.363961031 + 1 Combine like terms: -1 + 1 = 0 0 + n = 6.363961031 + 1 n = 6.363961031 + 1 Combine like terms: 6.363961031 + 1 = 7.363961031 n = 7.363961031 Simplifying n = 7.363961031Subproblem 2
n + -1 = -6.363961031 Simplifying n + -1 = -6.363961031 Reorder the terms: -1 + n = -6.363961031 Solving -1 + n = -6.363961031 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -6.363961031 + 1 Combine like terms: -1 + 1 = 0 0 + n = -6.363961031 + 1 n = -6.363961031 + 1 Combine like terms: -6.363961031 + 1 = -5.363961031 n = -5.363961031 Simplifying n = -5.363961031Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.363961031, -5.363961031}
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