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Simplifying n2 + 18n + -34 = 0 Reorder the terms: -34 + 18n + n2 = 0 Solving -34 + 18n + n2 = 0 Solving for variable 'n'. 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 = 115 81 + 18n + n2 = 115 Factor a perfect square on the left side: (n + 9)(n + 9) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (n + 9) equal to 10.723805295 and -10.723805295.Subproblem 1
n + 9 = 10.723805295 Simplifying n + 9 = 10.723805295 Reorder the terms: 9 + n = 10.723805295 Solving 9 + n = 10.723805295 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 = 10.723805295 + -9 Combine like terms: 9 + -9 = 0 0 + n = 10.723805295 + -9 n = 10.723805295 + -9 Combine like terms: 10.723805295 + -9 = 1.723805295 n = 1.723805295 Simplifying n = 1.723805295Subproblem 2
n + 9 = -10.723805295 Simplifying n + 9 = -10.723805295 Reorder the terms: 9 + n = -10.723805295 Solving 9 + n = -10.723805295 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 = -10.723805295 + -9 Combine like terms: 9 + -9 = 0 0 + n = -10.723805295 + -9 n = -10.723805295 + -9 Combine like terms: -10.723805295 + -9 = -19.723805295 n = -19.723805295 Simplifying n = -19.723805295Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.723805295, -19.723805295}
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