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Simplifying N(0.01717 + 0.00002828N) = 1 (0.01717 * N + 0.00002828N * N) = 1 (0.01717N + 0.00002828N2) = 1 Solving 0.01717N + 0.00002828N2 = 1 Solving for variable 'N'. Reorder the terms: -1 + 0.01717N + 0.00002828N2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 0.01717N + 0.00002828N2 = 0 Begin completing the square. Divide all terms by 0.00002828 the coefficient of the squared term: Divide each side by '0.00002828'. -35360.67893 + 607.1428571N + N2 = 0 Move the constant term to the right: Add '35360.67893' to each side of the equation. -35360.67893 + 607.1428571N + 35360.67893 + N2 = 0 + 35360.67893 Reorder the terms: -35360.67893 + 35360.67893 + 607.1428571N + N2 = 0 + 35360.67893 Combine like terms: -35360.67893 + 35360.67893 = 0.00000 0.00000 + 607.1428571N + N2 = 0 + 35360.67893 607.1428571N + N2 = 0 + 35360.67893 Combine like terms: 0 + 35360.67893 = 35360.67893 607.1428571N + N2 = 35360.67893 The N term is 607.1428571N. Take half its coefficient (303.5714286). Square it (92155.61226) and add it to both sides. Add '92155.61226' to each side of the equation. 607.1428571N + 92155.61226 + N2 = 35360.67893 + 92155.61226 Reorder the terms: 92155.61226 + 607.1428571N + N2 = 35360.67893 + 92155.61226 Combine like terms: 35360.67893 + 92155.61226 = 127516.29119 92155.61226 + 607.1428571N + N2 = 127516.29119 Factor a perfect square on the left side: (N + 303.5714286)(N + 303.5714286) = 127516.29119 Calculate the square root of the right side: 357.094232927 Break this problem into two subproblems by setting (N + 303.5714286) equal to 357.094232927 and -357.094232927.Subproblem 1
N + 303.5714286 = 357.094232927 Simplifying N + 303.5714286 = 357.094232927 Reorder the terms: 303.5714286 + N = 357.094232927 Solving 303.5714286 + N = 357.094232927 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-303.5714286' to each side of the equation. 303.5714286 + -303.5714286 + N = 357.094232927 + -303.5714286 Combine like terms: 303.5714286 + -303.5714286 = 0.0000000 0.0000000 + N = 357.094232927 + -303.5714286 N = 357.094232927 + -303.5714286 Combine like terms: 357.094232927 + -303.5714286 = 53.522804327 N = 53.522804327 Simplifying N = 53.522804327Subproblem 2
N + 303.5714286 = -357.094232927 Simplifying N + 303.5714286 = -357.094232927 Reorder the terms: 303.5714286 + N = -357.094232927 Solving 303.5714286 + N = -357.094232927 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-303.5714286' to each side of the equation. 303.5714286 + -303.5714286 + N = -357.094232927 + -303.5714286 Combine like terms: 303.5714286 + -303.5714286 = 0.0000000 0.0000000 + N = -357.094232927 + -303.5714286 N = -357.094232927 + -303.5714286 Combine like terms: -357.094232927 + -303.5714286 = -660.665661527 N = -660.665661527 Simplifying N = -660.665661527Solution
The solution to the problem is based on the solutions from the subproblems. N = {53.522804327, -660.665661527}
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