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Simplifying n2 + 18n + -55 = 0 Reorder the terms: -55 + 18n + n2 = 0 Solving -55 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 18n + 55 + n2 = 0 + 55 Reorder the terms: -55 + 55 + 18n + n2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 18n + n2 = 0 + 55 18n + n2 = 0 + 55 Combine like terms: 0 + 55 = 55 18n + n2 = 55 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 = 55 + 81 Reorder the terms: 81 + 18n + n2 = 55 + 81 Combine like terms: 55 + 81 = 136 81 + 18n + n2 = 136 Factor a perfect square on the left side: (n + 9)(n + 9) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (n + 9) equal to 11.66190379 and -11.66190379.Subproblem 1
n + 9 = 11.66190379 Simplifying n + 9 = 11.66190379 Reorder the terms: 9 + n = 11.66190379 Solving 9 + n = 11.66190379 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 = 11.66190379 + -9 Combine like terms: 9 + -9 = 0 0 + n = 11.66190379 + -9 n = 11.66190379 + -9 Combine like terms: 11.66190379 + -9 = 2.66190379 n = 2.66190379 Simplifying n = 2.66190379Subproblem 2
n + 9 = -11.66190379 Simplifying n + 9 = -11.66190379 Reorder the terms: 9 + n = -11.66190379 Solving 9 + n = -11.66190379 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 = -11.66190379 + -9 Combine like terms: 9 + -9 = 0 0 + n = -11.66190379 + -9 n = -11.66190379 + -9 Combine like terms: -11.66190379 + -9 = -20.66190379 n = -20.66190379 Simplifying n = -20.66190379Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.66190379, -20.66190379}
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