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Simplifying n2 + n + -20350 = 0 Reorder the terms: -20350 + n + n2 = 0 Solving -20350 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '20350' to each side of the equation. -20350 + n + 20350 + n2 = 0 + 20350 Reorder the terms: -20350 + 20350 + n + n2 = 0 + 20350 Combine like terms: -20350 + 20350 = 0 0 + n + n2 = 0 + 20350 n + n2 = 0 + 20350 Combine like terms: 0 + 20350 = 20350 n + n2 = 20350 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 20350 + 0.25 Reorder the terms: 0.25 + n + n2 = 20350 + 0.25 Combine like terms: 20350 + 0.25 = 20350.25 0.25 + n + n2 = 20350.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 20350.25 Calculate the square root of the right side: 142.654302424 Break this problem into two subproblems by setting (n + 0.5) equal to 142.654302424 and -142.654302424.Subproblem 1
n + 0.5 = 142.654302424 Simplifying n + 0.5 = 142.654302424 Reorder the terms: 0.5 + n = 142.654302424 Solving 0.5 + n = 142.654302424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 142.654302424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 142.654302424 + -0.5 n = 142.654302424 + -0.5 Combine like terms: 142.654302424 + -0.5 = 142.154302424 n = 142.154302424 Simplifying n = 142.154302424Subproblem 2
n + 0.5 = -142.654302424 Simplifying n + 0.5 = -142.654302424 Reorder the terms: 0.5 + n = -142.654302424 Solving 0.5 + n = -142.654302424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -142.654302424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -142.654302424 + -0.5 n = -142.654302424 + -0.5 Combine like terms: -142.654302424 + -0.5 = -143.154302424 n = -143.154302424 Simplifying n = -143.154302424Solution
The solution to the problem is based on the solutions from the subproblems. n = {142.154302424, -143.154302424}
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