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Simplifying n2 + n + -92 = 0 Reorder the terms: -92 + n + n2 = 0 Solving -92 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + n + 92 + n2 = 0 + 92 Reorder the terms: -92 + 92 + n + n2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + n + n2 = 0 + 92 n + n2 = 0 + 92 Combine like terms: 0 + 92 = 92 n + n2 = 92 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 = 92 + 0.25 Reorder the terms: 0.25 + n + n2 = 92 + 0.25 Combine like terms: 92 + 0.25 = 92.25 0.25 + n + n2 = 92.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (n + 0.5) equal to 9.604686356 and -9.604686356.Subproblem 1
n + 0.5 = 9.604686356 Simplifying n + 0.5 = 9.604686356 Reorder the terms: 0.5 + n = 9.604686356 Solving 0.5 + n = 9.604686356 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 = 9.604686356 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 9.604686356 + -0.5 n = 9.604686356 + -0.5 Combine like terms: 9.604686356 + -0.5 = 9.104686356 n = 9.104686356 Simplifying n = 9.104686356Subproblem 2
n + 0.5 = -9.604686356 Simplifying n + 0.5 = -9.604686356 Reorder the terms: 0.5 + n = -9.604686356 Solving 0.5 + n = -9.604686356 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 = -9.604686356 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -9.604686356 + -0.5 n = -9.604686356 + -0.5 Combine like terms: -9.604686356 + -0.5 = -10.104686356 n = -10.104686356 Simplifying n = -10.104686356Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.104686356, -10.104686356}
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