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Simplifying n2 + -18n + 43 = 9 Reorder the terms: 43 + -18n + n2 = 9 Solving 43 + -18n + n2 = 9 Solving for variable 'n'. Reorder the terms: 43 + -9 + -18n + n2 = 9 + -9 Combine like terms: 43 + -9 = 34 34 + -18n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 34 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -18n + -34 + n2 = 0 + -34 Reorder the terms: 34 + -34 + -18n + n2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -18n + n2 = 0 + -34 -18n + n2 = 0 + -34 Combine like terms: 0 + -34 = -34 -18n + n2 = -34 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 = -34 + 81 Reorder the terms: 81 + -18n + n2 = -34 + 81 Combine like terms: -34 + 81 = 47 81 + -18n + n2 = 47 Factor a perfect square on the left side: (n + -9)(n + -9) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (n + -9) equal to 6.8556546 and -6.8556546.Subproblem 1
n + -9 = 6.8556546 Simplifying n + -9 = 6.8556546 Reorder the terms: -9 + n = 6.8556546 Solving -9 + n = 6.8556546 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 = 6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + n = 6.8556546 + 9 n = 6.8556546 + 9 Combine like terms: 6.8556546 + 9 = 15.8556546 n = 15.8556546 Simplifying n = 15.8556546Subproblem 2
n + -9 = -6.8556546 Simplifying n + -9 = -6.8556546 Reorder the terms: -9 + n = -6.8556546 Solving -9 + n = -6.8556546 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 = -6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + n = -6.8556546 + 9 n = -6.8556546 + 9 Combine like terms: -6.8556546 + 9 = 2.1443454 n = 2.1443454 Simplifying n = 2.1443454Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.8556546, 2.1443454}
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