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Simplifying n2 + -18n + 40 = 0 Reorder the terms: 40 + -18n + n2 = 0 Solving 40 + -18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -18n + -40 + n2 = 0 + -40 Reorder the terms: 40 + -40 + -18n + n2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -18n + n2 = 0 + -40 -18n + n2 = 0 + -40 Combine like terms: 0 + -40 = -40 -18n + n2 = -40 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 = -40 + 81 Reorder the terms: 81 + -18n + n2 = -40 + 81 Combine like terms: -40 + 81 = 41 81 + -18n + n2 = 41 Factor a perfect square on the left side: (n + -9)(n + -9) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (n + -9) equal to 6.403124237 and -6.403124237.Subproblem 1
n + -9 = 6.403124237 Simplifying n + -9 = 6.403124237 Reorder the terms: -9 + n = 6.403124237 Solving -9 + n = 6.403124237 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 = 6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + n = 6.403124237 + 9 n = 6.403124237 + 9 Combine like terms: 6.403124237 + 9 = 15.403124237 n = 15.403124237 Simplifying n = 15.403124237Subproblem 2
n + -9 = -6.403124237 Simplifying n + -9 = -6.403124237 Reorder the terms: -9 + n = -6.403124237 Solving -9 + n = -6.403124237 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 = -6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + n = -6.403124237 + 9 n = -6.403124237 + 9 Combine like terms: -6.403124237 + 9 = 2.596875763 n = 2.596875763 Simplifying n = 2.596875763Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.403124237, 2.596875763}
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