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Simplifying 2n2 + 4n + -141 = 0 Reorder the terms: -141 + 4n + 2n2 = 0 Solving -141 + 4n + 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'. -70.5 + 2n + n2 = 0 Move the constant term to the right: Add '70.5' to each side of the equation. -70.5 + 2n + 70.5 + n2 = 0 + 70.5 Reorder the terms: -70.5 + 70.5 + 2n + n2 = 0 + 70.5 Combine like terms: -70.5 + 70.5 = 0.0 0.0 + 2n + n2 = 0 + 70.5 2n + n2 = 0 + 70.5 Combine like terms: 0 + 70.5 = 70.5 2n + n2 = 70.5 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 70.5 + 1 Reorder the terms: 1 + 2n + n2 = 70.5 + 1 Combine like terms: 70.5 + 1 = 71.5 1 + 2n + n2 = 71.5 Factor a perfect square on the left side: (n + 1)(n + 1) = 71.5 Calculate the square root of the right side: 8.455767263 Break this problem into two subproblems by setting (n + 1) equal to 8.455767263 and -8.455767263.Subproblem 1
n + 1 = 8.455767263 Simplifying n + 1 = 8.455767263 Reorder the terms: 1 + n = 8.455767263 Solving 1 + n = 8.455767263 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 8.455767263 + -1 Combine like terms: 1 + -1 = 0 0 + n = 8.455767263 + -1 n = 8.455767263 + -1 Combine like terms: 8.455767263 + -1 = 7.455767263 n = 7.455767263 Simplifying n = 7.455767263Subproblem 2
n + 1 = -8.455767263 Simplifying n + 1 = -8.455767263 Reorder the terms: 1 + n = -8.455767263 Solving 1 + n = -8.455767263 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -8.455767263 + -1 Combine like terms: 1 + -1 = 0 0 + n = -8.455767263 + -1 n = -8.455767263 + -1 Combine like terms: -8.455767263 + -1 = -9.455767263 n = -9.455767263 Simplifying n = -9.455767263Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.455767263, -9.455767263}
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