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Simplifying N2 + -9N + -40 = 0 Reorder the terms: -40 + -9N + N2 = 0 Solving -40 + -9N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -9N + 40 + N2 = 0 + 40 Reorder the terms: -40 + 40 + -9N + N2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -9N + N2 = 0 + 40 -9N + N2 = 0 + 40 Combine like terms: 0 + 40 = 40 -9N + N2 = 40 The N term is -9N. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9N + 20.25 + N2 = 40 + 20.25 Reorder the terms: 20.25 + -9N + N2 = 40 + 20.25 Combine like terms: 40 + 20.25 = 60.25 20.25 + -9N + N2 = 60.25 Factor a perfect square on the left side: (N + -4.5)(N + -4.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (N + -4.5) equal to 7.762087348 and -7.762087348.Subproblem 1
N + -4.5 = 7.762087348 Simplifying N + -4.5 = 7.762087348 Reorder the terms: -4.5 + N = 7.762087348 Solving -4.5 + N = 7.762087348 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + N = 7.762087348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + N = 7.762087348 + 4.5 N = 7.762087348 + 4.5 Combine like terms: 7.762087348 + 4.5 = 12.262087348 N = 12.262087348 Simplifying N = 12.262087348Subproblem 2
N + -4.5 = -7.762087348 Simplifying N + -4.5 = -7.762087348 Reorder the terms: -4.5 + N = -7.762087348 Solving -4.5 + N = -7.762087348 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + N = -7.762087348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + N = -7.762087348 + 4.5 N = -7.762087348 + 4.5 Combine like terms: -7.762087348 + 4.5 = -3.262087348 N = -3.262087348 Simplifying N = -3.262087348Solution
The solution to the problem is based on the solutions from the subproblems. N = {12.262087348, -3.262087348}
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