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Simplifying -1n2 + 18n + -14 = 0 Reorder the terms: -14 + 18n + -1n2 = 0 Solving -14 + 18n + -1n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -18n + n2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -18n + -14 + n2 = 0 + -14 Reorder the terms: 14 + -14 + -18n + n2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -18n + n2 = 0 + -14 -18n + n2 = 0 + -14 Combine like terms: 0 + -14 = -14 -18n + n2 = -14 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 = -14 + 81 Reorder the terms: 81 + -18n + n2 = -14 + 81 Combine like terms: -14 + 81 = 67 81 + -18n + n2 = 67 Factor a perfect square on the left side: (n + -9)(n + -9) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (n + -9) equal to 8.185352772 and -8.185352772.Subproblem 1
n + -9 = 8.185352772 Simplifying n + -9 = 8.185352772 Reorder the terms: -9 + n = 8.185352772 Solving -9 + n = 8.185352772 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 = 8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + n = 8.185352772 + 9 n = 8.185352772 + 9 Combine like terms: 8.185352772 + 9 = 17.185352772 n = 17.185352772 Simplifying n = 17.185352772Subproblem 2
n + -9 = -8.185352772 Simplifying n + -9 = -8.185352772 Reorder the terms: -9 + n = -8.185352772 Solving -9 + n = -8.185352772 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 = -8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + n = -8.185352772 + 9 n = -8.185352772 + 9 Combine like terms: -8.185352772 + 9 = 0.814647228 n = 0.814647228 Simplifying n = 0.814647228Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.185352772, 0.814647228}
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