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Simplifying N2 + N + -332 = 0 Reorder the terms: -332 + N + N2 = 0 Solving -332 + N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '332' to each side of the equation. -332 + N + 332 + N2 = 0 + 332 Reorder the terms: -332 + 332 + N + N2 = 0 + 332 Combine like terms: -332 + 332 = 0 0 + N + N2 = 0 + 332 N + N2 = 0 + 332 Combine like terms: 0 + 332 = 332 N + N2 = 332 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 = 332 + 0.25 Reorder the terms: 0.25 + N + N2 = 332 + 0.25 Combine like terms: 332 + 0.25 = 332.25 0.25 + N + N2 = 332.25 Factor a perfect square on the left side: (N + 0.5)(N + 0.5) = 332.25 Calculate the square root of the right side: 18.227726134 Break this problem into two subproblems by setting (N + 0.5) equal to 18.227726134 and -18.227726134.Subproblem 1
N + 0.5 = 18.227726134 Simplifying N + 0.5 = 18.227726134 Reorder the terms: 0.5 + N = 18.227726134 Solving 0.5 + N = 18.227726134 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 = 18.227726134 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + N = 18.227726134 + -0.5 N = 18.227726134 + -0.5 Combine like terms: 18.227726134 + -0.5 = 17.727726134 N = 17.727726134 Simplifying N = 17.727726134Subproblem 2
N + 0.5 = -18.227726134 Simplifying N + 0.5 = -18.227726134 Reorder the terms: 0.5 + N = -18.227726134 Solving 0.5 + N = -18.227726134 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 = -18.227726134 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + N = -18.227726134 + -0.5 N = -18.227726134 + -0.5 Combine like terms: -18.227726134 + -0.5 = -18.727726134 N = -18.727726134 Simplifying N = -18.727726134Solution
The solution to the problem is based on the solutions from the subproblems. N = {17.727726134, -18.727726134}
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