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Simplifying n2 + 17n + 35 = 0 Reorder the terms: 35 + 17n + n2 = 0 Solving 35 + 17n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 17n + -35 + n2 = 0 + -35 Reorder the terms: 35 + -35 + 17n + n2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 17n + n2 = 0 + -35 17n + n2 = 0 + -35 Combine like terms: 0 + -35 = -35 17n + n2 = -35 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 = -35 + 72.25 Reorder the terms: 72.25 + 17n + n2 = -35 + 72.25 Combine like terms: -35 + 72.25 = 37.25 72.25 + 17n + n2 = 37.25 Factor a perfect square on the left side: (n + 8.5)(n + 8.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (n + 8.5) equal to 6.103277808 and -6.103277808.Subproblem 1
n + 8.5 = 6.103277808 Simplifying n + 8.5 = 6.103277808 Reorder the terms: 8.5 + n = 6.103277808 Solving 8.5 + n = 6.103277808 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 = 6.103277808 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = 6.103277808 + -8.5 n = 6.103277808 + -8.5 Combine like terms: 6.103277808 + -8.5 = -2.396722192 n = -2.396722192 Simplifying n = -2.396722192Subproblem 2
n + 8.5 = -6.103277808 Simplifying n + 8.5 = -6.103277808 Reorder the terms: 8.5 + n = -6.103277808 Solving 8.5 + n = -6.103277808 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 = -6.103277808 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = -6.103277808 + -8.5 n = -6.103277808 + -8.5 Combine like terms: -6.103277808 + -8.5 = -14.603277808 n = -14.603277808 Simplifying n = -14.603277808Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.396722192, -14.603277808}
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