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Simplifying n2 + 2n + -1080 = 0 Reorder the terms: -1080 + 2n + n2 = 0 Solving -1080 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1080' to each side of the equation. -1080 + 2n + 1080 + n2 = 0 + 1080 Reorder the terms: -1080 + 1080 + 2n + n2 = 0 + 1080 Combine like terms: -1080 + 1080 = 0 0 + 2n + n2 = 0 + 1080 2n + n2 = 0 + 1080 Combine like terms: 0 + 1080 = 1080 2n + n2 = 1080 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 = 1080 + 1 Reorder the terms: 1 + 2n + n2 = 1080 + 1 Combine like terms: 1080 + 1 = 1081 1 + 2n + n2 = 1081 Factor a perfect square on the left side: (n + 1)(n + 1) = 1081 Calculate the square root of the right side: 32.878564446 Break this problem into two subproblems by setting (n + 1) equal to 32.878564446 and -32.878564446.Subproblem 1
n + 1 = 32.878564446 Simplifying n + 1 = 32.878564446 Reorder the terms: 1 + n = 32.878564446 Solving 1 + n = 32.878564446 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 = 32.878564446 + -1 Combine like terms: 1 + -1 = 0 0 + n = 32.878564446 + -1 n = 32.878564446 + -1 Combine like terms: 32.878564446 + -1 = 31.878564446 n = 31.878564446 Simplifying n = 31.878564446Subproblem 2
n + 1 = -32.878564446 Simplifying n + 1 = -32.878564446 Reorder the terms: 1 + n = -32.878564446 Solving 1 + n = -32.878564446 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 = -32.878564446 + -1 Combine like terms: 1 + -1 = 0 0 + n = -32.878564446 + -1 n = -32.878564446 + -1 Combine like terms: -32.878564446 + -1 = -33.878564446 n = -33.878564446 Simplifying n = -33.878564446Solution
The solution to the problem is based on the solutions from the subproblems. n = {31.878564446, -33.878564446}
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