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Simplifying n2 + 17n + -2000 = 0 Reorder the terms: -2000 + 17n + n2 = 0 Solving -2000 + 17n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 17n + 2000 + n2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 17n + n2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 17n + n2 = 0 + 2000 17n + n2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 17n + n2 = 2000 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 = 2000 + 72.25 Reorder the terms: 72.25 + 17n + n2 = 2000 + 72.25 Combine like terms: 2000 + 72.25 = 2072.25 72.25 + 17n + n2 = 2072.25 Factor a perfect square on the left side: (n + 8.5)(n + 8.5) = 2072.25 Calculate the square root of the right side: 45.521972716 Break this problem into two subproblems by setting (n + 8.5) equal to 45.521972716 and -45.521972716.Subproblem 1
n + 8.5 = 45.521972716 Simplifying n + 8.5 = 45.521972716 Reorder the terms: 8.5 + n = 45.521972716 Solving 8.5 + n = 45.521972716 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 = 45.521972716 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = 45.521972716 + -8.5 n = 45.521972716 + -8.5 Combine like terms: 45.521972716 + -8.5 = 37.021972716 n = 37.021972716 Simplifying n = 37.021972716Subproblem 2
n + 8.5 = -45.521972716 Simplifying n + 8.5 = -45.521972716 Reorder the terms: 8.5 + n = -45.521972716 Solving 8.5 + n = -45.521972716 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 = -45.521972716 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + n = -45.521972716 + -8.5 n = -45.521972716 + -8.5 Combine like terms: -45.521972716 + -8.5 = -54.021972716 n = -54.021972716 Simplifying n = -54.021972716Solution
The solution to the problem is based on the solutions from the subproblems. n = {37.021972716, -54.021972716}
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