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Simplifying n2 + 10n + 25 = 40 Reorder the terms: 25 + 10n + n2 = 40 Solving 25 + 10n + n2 = 40 Solving for variable 'n'. Reorder the terms: 25 + -40 + 10n + n2 = 40 + -40 Combine like terms: 25 + -40 = -15 -15 + 10n + n2 = 40 + -40 Combine like terms: 40 + -40 = 0 -15 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 10n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + 10n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 10n + n2 = 0 + 15 10n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 10n + n2 = 15 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = 15 + 25 Reorder the terms: 25 + 10n + n2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + 10n + n2 = 40 Factor a perfect square on the left side: (n + 5)(n + 5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (n + 5) equal to 6.32455532 and -6.32455532.Subproblem 1
n + 5 = 6.32455532 Simplifying n + 5 = 6.32455532 Reorder the terms: 5 + n = 6.32455532 Solving 5 + n = 6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + n = 6.32455532 + -5 n = 6.32455532 + -5 Combine like terms: 6.32455532 + -5 = 1.32455532 n = 1.32455532 Simplifying n = 1.32455532Subproblem 2
n + 5 = -6.32455532 Simplifying n + 5 = -6.32455532 Reorder the terms: 5 + n = -6.32455532 Solving 5 + n = -6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + n = -6.32455532 + -5 n = -6.32455532 + -5 Combine like terms: -6.32455532 + -5 = -11.32455532 n = -11.32455532 Simplifying n = -11.32455532Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.32455532, -11.32455532}
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