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Simplifying (n + -5)(n + -5) = 7 Reorder the terms: (-5 + n)(n + -5) = 7 Reorder the terms: (-5 + n)(-5 + n) = 7 Multiply (-5 + n) * (-5 + n) (-5(-5 + n) + n(-5 + n)) = 7 ((-5 * -5 + n * -5) + n(-5 + n)) = 7 ((25 + -5n) + n(-5 + n)) = 7 (25 + -5n + (-5 * n + n * n)) = 7 (25 + -5n + (-5n + n2)) = 7 Combine like terms: -5n + -5n = -10n (25 + -10n + n2) = 7 Solving 25 + -10n + n2 = 7 Solving for variable 'n'. Reorder the terms: 25 + -7 + -10n + n2 = 7 + -7 Combine like terms: 25 + -7 = 18 18 + -10n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 18 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10n + -18 + n2 = 0 + -18 Reorder the terms: 18 + -18 + -10n + n2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10n + n2 = 0 + -18 -10n + n2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10n + n2 = -18 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 = -18 + 25 Reorder the terms: 25 + -10n + n2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10n + n2 = 7 Factor a perfect square on the left side: (n + -5)(n + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (n + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
n + -5 = 2.645751311 Simplifying n + -5 = 2.645751311 Reorder the terms: -5 + n = 2.645751311 Solving -5 + n = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + n = 2.645751311 + 5 n = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 n = 7.645751311 Simplifying n = 7.645751311Subproblem 2
n + -5 = -2.645751311 Simplifying n + -5 = -2.645751311 Reorder the terms: -5 + n = -2.645751311 Solving -5 + n = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + n = -2.645751311 + 5 n = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 n = 2.354248689 Simplifying n = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.645751311, 2.354248689}
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