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Simplifying n2 + n + -100 = 0 Reorder the terms: -100 + n + n2 = 0 Solving -100 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + n + 100 + n2 = 0 + 100 Reorder the terms: -100 + 100 + n + n2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + n + n2 = 0 + 100 n + n2 = 0 + 100 Combine like terms: 0 + 100 = 100 n + n2 = 100 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 = 100 + 0.25 Reorder the terms: 0.25 + n + n2 = 100 + 0.25 Combine like terms: 100 + 0.25 = 100.25 0.25 + n + n2 = 100.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (n + 0.5) equal to 10.012492197 and -10.012492197.Subproblem 1
n + 0.5 = 10.012492197 Simplifying n + 0.5 = 10.012492197 Reorder the terms: 0.5 + n = 10.012492197 Solving 0.5 + n = 10.012492197 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 = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 10.012492197 + -0.5 n = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 n = 9.512492197 Simplifying n = 9.512492197Subproblem 2
n + 0.5 = -10.012492197 Simplifying n + 0.5 = -10.012492197 Reorder the terms: 0.5 + n = -10.012492197 Solving 0.5 + n = -10.012492197 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 = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -10.012492197 + -0.5 n = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 n = -10.512492197 Simplifying n = -10.512492197Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.512492197, -10.512492197}
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