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Simplifying n2 + 17n + 6 = 0 Reorder the terms: 6 + 17n + n2 = 0 Solving 6 + 17n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 17n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 17n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 17n + n2 = 0 + -6 17n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 17n + n2 = -6 The n term is 17n. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17n + 72.25 + n2 = -6 + 72.25 Reorder the terms: 72.25 + 17n + n2 = -6 + 72.25 Combine like terms: -6 + 72.25 = 66.25 72.25 + 17n + n2 = 66.25 Factor a perfect square on the left side: (n + 8.5)(n + 8.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (n + 8.5) equal to 8.139410298 and -8.139410298.Subproblem 1
n + 8.5 = 8.139410298 Simplifying n + 8.5 = 8.139410298 Reorder the terms: 8.5 + n = 8.139410298 Solving 8.5 + n = 8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + n = 8.139410298 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = 8.139410298 + -8.5 n = 8.139410298 + -8.5 Combine like terms: 8.139410298 + -8.5 = -0.360589702 n = -0.360589702 Simplifying n = -0.360589702Subproblem 2
n + 8.5 = -8.139410298 Simplifying n + 8.5 = -8.139410298 Reorder the terms: 8.5 + n = -8.139410298 Solving 8.5 + n = -8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + n = -8.139410298 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = -8.139410298 + -8.5 n = -8.139410298 + -8.5 Combine like terms: -8.139410298 + -8.5 = -16.639410298 n = -16.639410298 Simplifying n = -16.639410298Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.360589702, -16.639410298}
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