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Simplifying n2 + 2n + -41 = 0 Reorder the terms: -41 + 2n + n2 = 0 Solving -41 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 2n + 41 + n2 = 0 + 41 Reorder the terms: -41 + 41 + 2n + n2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 2n + n2 = 0 + 41 2n + n2 = 0 + 41 Combine like terms: 0 + 41 = 41 2n + n2 = 41 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 = 41 + 1 Reorder the terms: 1 + 2n + n2 = 41 + 1 Combine like terms: 41 + 1 = 42 1 + 2n + n2 = 42 Factor a perfect square on the left side: (n + 1)(n + 1) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (n + 1) equal to 6.480740698 and -6.480740698.Subproblem 1
n + 1 = 6.480740698 Simplifying n + 1 = 6.480740698 Reorder the terms: 1 + n = 6.480740698 Solving 1 + n = 6.480740698 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 = 6.480740698 + -1 Combine like terms: 1 + -1 = 0 0 + n = 6.480740698 + -1 n = 6.480740698 + -1 Combine like terms: 6.480740698 + -1 = 5.480740698 n = 5.480740698 Simplifying n = 5.480740698Subproblem 2
n + 1 = -6.480740698 Simplifying n + 1 = -6.480740698 Reorder the terms: 1 + n = -6.480740698 Solving 1 + n = -6.480740698 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 = -6.480740698 + -1 Combine like terms: 1 + -1 = 0 0 + n = -6.480740698 + -1 n = -6.480740698 + -1 Combine like terms: -6.480740698 + -1 = -7.480740698 n = -7.480740698 Simplifying n = -7.480740698Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.480740698, -7.480740698}
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