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Simplifying n2 + 18n = -5 Reorder the terms: 18n + n2 = -5 Solving 18n + n2 = -5 Solving for variable 'n'. Reorder the terms: 5 + 18n + n2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 18n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 18n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 18n + n2 = 0 + -5 18n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 18n + n2 = -5 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 = -5 + 81 Reorder the terms: 81 + 18n + n2 = -5 + 81 Combine like terms: -5 + 81 = 76 81 + 18n + n2 = 76 Factor a perfect square on the left side: (n + 9)(n + 9) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (n + 9) equal to 8.717797887 and -8.717797887.Subproblem 1
n + 9 = 8.717797887 Simplifying n + 9 = 8.717797887 Reorder the terms: 9 + n = 8.717797887 Solving 9 + n = 8.717797887 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 = 8.717797887 + -9 Combine like terms: 9 + -9 = 0 0 + n = 8.717797887 + -9 n = 8.717797887 + -9 Combine like terms: 8.717797887 + -9 = -0.282202113 n = -0.282202113 Simplifying n = -0.282202113Subproblem 2
n + 9 = -8.717797887 Simplifying n + 9 = -8.717797887 Reorder the terms: 9 + n = -8.717797887 Solving 9 + n = -8.717797887 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 = -8.717797887 + -9 Combine like terms: 9 + -9 = 0 0 + n = -8.717797887 + -9 n = -8.717797887 + -9 Combine like terms: -8.717797887 + -9 = -17.717797887 n = -17.717797887 Simplifying n = -17.717797887Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.282202113, -17.717797887}
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