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Simplifying n2 + 2n = 1200 Reorder the terms: 2n + n2 = 1200 Solving 2n + n2 = 1200 Solving for variable 'n'. Reorder the terms: -1200 + 2n + n2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 -1200 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 2n + 1200 + n2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 2n + n2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 2n + n2 = 0 + 1200 2n + n2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 2n + n2 = 1200 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 = 1200 + 1 Reorder the terms: 1 + 2n + n2 = 1200 + 1 Combine like terms: 1200 + 1 = 1201 1 + 2n + n2 = 1201 Factor a perfect square on the left side: (n + 1)(n + 1) = 1201 Calculate the square root of the right side: 34.655446902 Break this problem into two subproblems by setting (n + 1) equal to 34.655446902 and -34.655446902.Subproblem 1
n + 1 = 34.655446902 Simplifying n + 1 = 34.655446902 Reorder the terms: 1 + n = 34.655446902 Solving 1 + n = 34.655446902 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 = 34.655446902 + -1 Combine like terms: 1 + -1 = 0 0 + n = 34.655446902 + -1 n = 34.655446902 + -1 Combine like terms: 34.655446902 + -1 = 33.655446902 n = 33.655446902 Simplifying n = 33.655446902Subproblem 2
n + 1 = -34.655446902 Simplifying n + 1 = -34.655446902 Reorder the terms: 1 + n = -34.655446902 Solving 1 + n = -34.655446902 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 = -34.655446902 + -1 Combine like terms: 1 + -1 = 0 0 + n = -34.655446902 + -1 n = -34.655446902 + -1 Combine like terms: -34.655446902 + -1 = -35.655446902 n = -35.655446902 Simplifying n = -35.655446902Solution
The solution to the problem is based on the solutions from the subproblems. n = {33.655446902, -35.655446902}
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