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Simplifying n2 + 201n + -2700 = 0 Reorder the terms: -2700 + 201n + n2 = 0 Solving -2700 + 201n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + 201n + 2700 + n2 = 0 + 2700 Reorder the terms: -2700 + 2700 + 201n + n2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + 201n + n2 = 0 + 2700 201n + n2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 201n + n2 = 2700 The n term is 201n. Take half its coefficient (100.5). Square it (10100.25) and add it to both sides. Add '10100.25' to each side of the equation. 201n + 10100.25 + n2 = 2700 + 10100.25 Reorder the terms: 10100.25 + 201n + n2 = 2700 + 10100.25 Combine like terms: 2700 + 10100.25 = 12800.25 10100.25 + 201n + n2 = 12800.25 Factor a perfect square on the left side: (n + 100.5)(n + 100.5) = 12800.25 Calculate the square root of the right side: 113.138189839 Break this problem into two subproblems by setting (n + 100.5) equal to 113.138189839 and -113.138189839.Subproblem 1
n + 100.5 = 113.138189839 Simplifying n + 100.5 = 113.138189839 Reorder the terms: 100.5 + n = 113.138189839 Solving 100.5 + n = 113.138189839 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-100.5' to each side of the equation. 100.5 + -100.5 + n = 113.138189839 + -100.5 Combine like terms: 100.5 + -100.5 = 0.0 0.0 + n = 113.138189839 + -100.5 n = 113.138189839 + -100.5 Combine like terms: 113.138189839 + -100.5 = 12.638189839 n = 12.638189839 Simplifying n = 12.638189839Subproblem 2
n + 100.5 = -113.138189839 Simplifying n + 100.5 = -113.138189839 Reorder the terms: 100.5 + n = -113.138189839 Solving 100.5 + n = -113.138189839 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-100.5' to each side of the equation. 100.5 + -100.5 + n = -113.138189839 + -100.5 Combine like terms: 100.5 + -100.5 = 0.0 0.0 + n = -113.138189839 + -100.5 n = -113.138189839 + -100.5 Combine like terms: -113.138189839 + -100.5 = -213.638189839 n = -213.638189839 Simplifying n = -213.638189839Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.638189839, -213.638189839}
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