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Simplifying n2 + 2n + -25.021 = 0 Reorder the terms: -25.021 + 2n + n2 = 0 Solving -25.021 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '25.021' to each side of the equation. -25.021 + 2n + 25.021 + n2 = 0 + 25.021 Reorder the terms: -25.021 + 25.021 + 2n + n2 = 0 + 25.021 Combine like terms: -25.021 + 25.021 = 0.000 0.000 + 2n + n2 = 0 + 25.021 2n + n2 = 0 + 25.021 Combine like terms: 0 + 25.021 = 25.021 2n + n2 = 25.021 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 = 25.021 + 1 Reorder the terms: 1 + 2n + n2 = 25.021 + 1 Combine like terms: 25.021 + 1 = 26.021 1 + 2n + n2 = 26.021 Factor a perfect square on the left side: (n + 1)(n + 1) = 26.021 Calculate the square root of the right side: 5.101078317 Break this problem into two subproblems by setting (n + 1) equal to 5.101078317 and -5.101078317.Subproblem 1
n + 1 = 5.101078317 Simplifying n + 1 = 5.101078317 Reorder the terms: 1 + n = 5.101078317 Solving 1 + n = 5.101078317 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 = 5.101078317 + -1 Combine like terms: 1 + -1 = 0 0 + n = 5.101078317 + -1 n = 5.101078317 + -1 Combine like terms: 5.101078317 + -1 = 4.101078317 n = 4.101078317 Simplifying n = 4.101078317Subproblem 2
n + 1 = -5.101078317 Simplifying n + 1 = -5.101078317 Reorder the terms: 1 + n = -5.101078317 Solving 1 + n = -5.101078317 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 = -5.101078317 + -1 Combine like terms: 1 + -1 = 0 0 + n = -5.101078317 + -1 n = -5.101078317 + -1 Combine like terms: -5.101078317 + -1 = -6.101078317 n = -6.101078317 Simplifying n = -6.101078317Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.101078317, -6.101078317}
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