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Simplifying n2 + -1n + -99 = 0 Reorder the terms: -99 + -1n + n2 = 0 Solving -99 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -1n + 99 + n2 = 0 + 99 Reorder the terms: -99 + 99 + -1n + n2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -1n + n2 = 0 + 99 -1n + n2 = 0 + 99 Combine like terms: 0 + 99 = 99 -1n + n2 = 99 The n term is -1n. 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. -1n + 0.25 + n2 = 99 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 99 + 0.25 Combine like terms: 99 + 0.25 = 99.25 0.25 + -1n + n2 = 99.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (n + -0.5) equal to 9.962429423 and -9.962429423.Subproblem 1
n + -0.5 = 9.962429423 Simplifying n + -0.5 = 9.962429423 Reorder the terms: -0.5 + n = 9.962429423 Solving -0.5 + n = 9.962429423 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 = 9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 9.962429423 + 0.5 n = 9.962429423 + 0.5 Combine like terms: 9.962429423 + 0.5 = 10.462429423 n = 10.462429423 Simplifying n = 10.462429423Subproblem 2
n + -0.5 = -9.962429423 Simplifying n + -0.5 = -9.962429423 Reorder the terms: -0.5 + n = -9.962429423 Solving -0.5 + n = -9.962429423 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 = -9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -9.962429423 + 0.5 n = -9.962429423 + 0.5 Combine like terms: -9.962429423 + 0.5 = -9.462429423 n = -9.462429423 Simplifying n = -9.462429423Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.462429423, -9.462429423}
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