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Simplifying n2 + 18n + -16 = 0 Reorder the terms: -16 + 18n + n2 = 0 Solving -16 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 18n + 16 + n2 = 0 + 16 Reorder the terms: -16 + 16 + 18n + n2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 18n + n2 = 0 + 16 18n + n2 = 0 + 16 Combine like terms: 0 + 16 = 16 18n + n2 = 16 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 = 16 + 81 Reorder the terms: 81 + 18n + n2 = 16 + 81 Combine like terms: 16 + 81 = 97 81 + 18n + n2 = 97 Factor a perfect square on the left side: (n + 9)(n + 9) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (n + 9) equal to 9.848857802 and -9.848857802.Subproblem 1
n + 9 = 9.848857802 Simplifying n + 9 = 9.848857802 Reorder the terms: 9 + n = 9.848857802 Solving 9 + n = 9.848857802 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 = 9.848857802 + -9 Combine like terms: 9 + -9 = 0 0 + n = 9.848857802 + -9 n = 9.848857802 + -9 Combine like terms: 9.848857802 + -9 = 0.848857802 n = 0.848857802 Simplifying n = 0.848857802Subproblem 2
n + 9 = -9.848857802 Simplifying n + 9 = -9.848857802 Reorder the terms: 9 + n = -9.848857802 Solving 9 + n = -9.848857802 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 = -9.848857802 + -9 Combine like terms: 9 + -9 = 0 0 + n = -9.848857802 + -9 n = -9.848857802 + -9 Combine like terms: -9.848857802 + -9 = -18.848857802 n = -18.848857802 Simplifying n = -18.848857802Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.848857802, -18.848857802}
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