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Simplifying n2 + n + -99 = 0 Reorder the terms: -99 + n + n2 = 0 Solving -99 + n + 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 + n + 99 + n2 = 0 + 99 Reorder the terms: -99 + 99 + n + n2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + n + n2 = 0 + 99 n + n2 = 0 + 99 Combine like terms: 0 + 99 = 99 n + n2 = 99 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 = 99 + 0.25 Reorder the terms: 0.25 + n + n2 = 99 + 0.25 Combine like terms: 99 + 0.25 = 99.25 0.25 + n + 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 = 9.462429423 n = 9.462429423 Simplifying n = 9.462429423Subproblem 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 = -10.462429423 n = -10.462429423 Simplifying n = -10.462429423Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.462429423, -10.462429423}
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