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Simplifying 200 + -1n + -1n2 = 0 Solving 200 + -1n + -1n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + n + n2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + n + 200 + n2 = 0 + 200 Reorder the terms: -200 + 200 + n + n2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + n + n2 = 0 + 200 n + n2 = 0 + 200 Combine like terms: 0 + 200 = 200 n + n2 = 200 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. + 0.25 + n2 = 200 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 1.25 + n2 = 200.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (n + 0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
n + 0.5 = 14.150971698 Simplifying n + 0.5 = 14.150971698 Reorder the terms: 0.5 + n = 14.150971698 Solving 0.5 + n = 14.150971698 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 = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 14.150971698 + -0.5 n = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 n = 13.650971698 Simplifying n = 13.650971698Subproblem 2
n + 0.5 = -14.150971698 Simplifying n + 0.5 = -14.150971698 Reorder the terms: 0.5 + n = -14.150971698 Solving 0.5 + n = -14.150971698 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 = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -14.150971698 + -0.5 n = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 n = -14.650971698 Simplifying n = -14.650971698Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.650971698, -14.650971698}
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