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Simplifying n2 + 18n + 8 = 0 Reorder the terms: 8 + 18n + n2 = 0 Solving 8 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 18n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + 18n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 18n + n2 = 0 + -8 18n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 18n + n2 = -8 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 = -8 + 81 Reorder the terms: 81 + 18n + n2 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + 18n + n2 = 73 Factor a perfect square on the left side: (n + 9)(n + 9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (n + 9) equal to 8.544003745 and -8.544003745.Subproblem 1
n + 9 = 8.544003745 Simplifying n + 9 = 8.544003745 Reorder the terms: 9 + n = 8.544003745 Solving 9 + n = 8.544003745 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 = 8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + n = 8.544003745 + -9 n = 8.544003745 + -9 Combine like terms: 8.544003745 + -9 = -0.455996255 n = -0.455996255 Simplifying n = -0.455996255Subproblem 2
n + 9 = -8.544003745 Simplifying n + 9 = -8.544003745 Reorder the terms: 9 + n = -8.544003745 Solving 9 + n = -8.544003745 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 = -8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + n = -8.544003745 + -9 n = -8.544003745 + -9 Combine like terms: -8.544003745 + -9 = -17.544003745 n = -17.544003745 Simplifying n = -17.544003745Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.455996255, -17.544003745}
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