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Simplifying n2 + 18n + 50 = 9 Reorder the terms: 50 + 18n + n2 = 9 Solving 50 + 18n + n2 = 9 Solving for variable 'n'. Reorder the terms: 50 + -9 + 18n + n2 = 9 + -9 Combine like terms: 50 + -9 = 41 41 + 18n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 41 + 18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 18n + -41 + n2 = 0 + -41 Reorder the terms: 41 + -41 + 18n + n2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 18n + n2 = 0 + -41 18n + n2 = 0 + -41 Combine like terms: 0 + -41 = -41 18n + n2 = -41 The n term is 18n. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18n + 81 + n2 = -41 + 81 Reorder the terms: 81 + 18n + n2 = -41 + 81 Combine like terms: -41 + 81 = 40 81 + 18n + n2 = 40 Factor a perfect square on the left side: (n + 9)(n + 9) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (n + 9) equal to 6.32455532 and -6.32455532.Subproblem 1
n + 9 = 6.32455532 Simplifying n + 9 = 6.32455532 Reorder the terms: 9 + n = 6.32455532 Solving 9 + n = 6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = 6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + n = 6.32455532 + -9 n = 6.32455532 + -9 Combine like terms: 6.32455532 + -9 = -2.67544468 n = -2.67544468 Simplifying n = -2.67544468Subproblem 2
n + 9 = -6.32455532 Simplifying n + 9 = -6.32455532 Reorder the terms: 9 + n = -6.32455532 Solving 9 + n = -6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = -6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + n = -6.32455532 + -9 n = -6.32455532 + -9 Combine like terms: -6.32455532 + -9 = -15.32455532 n = -15.32455532 Simplifying n = -15.32455532Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.67544468, -15.32455532}
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