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Simplifying 2n2 + -39n + -184 = 0 Reorder the terms: -184 + -39n + 2n2 = 0 Solving -184 + -39n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -92 + -19.5n + n2 = 0 Move the constant term to the right: Add '92' to each side of the equation. -92 + -19.5n + 92 + n2 = 0 + 92 Reorder the terms: -92 + 92 + -19.5n + n2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -19.5n + n2 = 0 + 92 -19.5n + n2 = 0 + 92 Combine like terms: 0 + 92 = 92 -19.5n + n2 = 92 The n term is -19.5n. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5n + 95.0625 + n2 = 92 + 95.0625 Reorder the terms: 95.0625 + -19.5n + n2 = 92 + 95.0625 Combine like terms: 92 + 95.0625 = 187.0625 95.0625 + -19.5n + n2 = 187.0625 Factor a perfect square on the left side: (n + -9.75)(n + -9.75) = 187.0625 Calculate the square root of the right side: 13.677079367 Break this problem into two subproblems by setting (n + -9.75) equal to 13.677079367 and -13.677079367.Subproblem 1
n + -9.75 = 13.677079367 Simplifying n + -9.75 = 13.677079367 Reorder the terms: -9.75 + n = 13.677079367 Solving -9.75 + n = 13.677079367 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + n = 13.677079367 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + n = 13.677079367 + 9.75 n = 13.677079367 + 9.75 Combine like terms: 13.677079367 + 9.75 = 23.427079367 n = 23.427079367 Simplifying n = 23.427079367Subproblem 2
n + -9.75 = -13.677079367 Simplifying n + -9.75 = -13.677079367 Reorder the terms: -9.75 + n = -13.677079367 Solving -9.75 + n = -13.677079367 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + n = -13.677079367 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + n = -13.677079367 + 9.75 n = -13.677079367 + 9.75 Combine like terms: -13.677079367 + 9.75 = -3.927079367 n = -3.927079367 Simplifying n = -3.927079367Solution
The solution to the problem is based on the solutions from the subproblems. n = {23.427079367, -3.927079367}
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