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Simplifying n2 + 2n + -38 = 0 Reorder the terms: -38 + 2n + n2 = 0 Solving -38 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 2n + 38 + n2 = 0 + 38 Reorder the terms: -38 + 38 + 2n + n2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2n + n2 = 0 + 38 2n + n2 = 0 + 38 Combine like terms: 0 + 38 = 38 2n + n2 = 38 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 = 38 + 1 Reorder the terms: 1 + 2n + n2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2n + n2 = 39 Factor a perfect square on the left side: (n + 1)(n + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (n + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
n + 1 = 6.244997998 Simplifying n + 1 = 6.244997998 Reorder the terms: 1 + n = 6.244997998 Solving 1 + n = 6.244997998 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 = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + n = 6.244997998 + -1 n = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 n = 5.244997998 Simplifying n = 5.244997998Subproblem 2
n + 1 = -6.244997998 Simplifying n + 1 = -6.244997998 Reorder the terms: 1 + n = -6.244997998 Solving 1 + n = -6.244997998 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 = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + n = -6.244997998 + -1 n = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 n = -7.244997998 Simplifying n = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.244997998, -7.244997998}
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