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Simplifying n2 + 18n + -90 = 0 Reorder the terms: -90 + 18n + n2 = 0 Solving -90 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 18n + 90 + n2 = 0 + 90 Reorder the terms: -90 + 90 + 18n + n2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 18n + n2 = 0 + 90 18n + n2 = 0 + 90 Combine like terms: 0 + 90 = 90 18n + n2 = 90 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 = 90 + 81 Reorder the terms: 81 + 18n + n2 = 90 + 81 Combine like terms: 90 + 81 = 171 81 + 18n + n2 = 171 Factor a perfect square on the left side: (n + 9)(n + 9) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (n + 9) equal to 13.076696831 and -13.076696831.Subproblem 1
n + 9 = 13.076696831 Simplifying n + 9 = 13.076696831 Reorder the terms: 9 + n = 13.076696831 Solving 9 + n = 13.076696831 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 = 13.076696831 + -9 Combine like terms: 9 + -9 = 0 0 + n = 13.076696831 + -9 n = 13.076696831 + -9 Combine like terms: 13.076696831 + -9 = 4.076696831 n = 4.076696831 Simplifying n = 4.076696831Subproblem 2
n + 9 = -13.076696831 Simplifying n + 9 = -13.076696831 Reorder the terms: 9 + n = -13.076696831 Solving 9 + n = -13.076696831 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 = -13.076696831 + -9 Combine like terms: 9 + -9 = 0 0 + n = -13.076696831 + -9 n = -13.076696831 + -9 Combine like terms: -13.076696831 + -9 = -22.076696831 n = -22.076696831 Simplifying n = -22.076696831Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.076696831, -22.076696831}
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