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Simplifying N2 + -9N = 18 Reorder the terms: -9N + N2 = 18 Solving -9N + N2 = 18 Solving for variable 'N'. Reorder the terms: -18 + -9N + N2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -9N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -9N + 18 + N2 = 0 + 18 Reorder the terms: -18 + 18 + -9N + N2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9N + N2 = 0 + 18 -9N + N2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9N + N2 = 18 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 = 18 + 20.25 Reorder the terms: 20.25 + -9N + N2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + -9N + N2 = 38.25 Factor a perfect square on the left side: (N + -4.5)(N + -4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (N + -4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
N + -4.5 = 6.184658438 Simplifying N + -4.5 = 6.184658438 Reorder the terms: -4.5 + N = 6.184658438 Solving -4.5 + N = 6.184658438 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 = 6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + N = 6.184658438 + 4.5 N = 6.184658438 + 4.5 Combine like terms: 6.184658438 + 4.5 = 10.684658438 N = 10.684658438 Simplifying N = 10.684658438Subproblem 2
N + -4.5 = -6.184658438 Simplifying N + -4.5 = -6.184658438 Reorder the terms: -4.5 + N = -6.184658438 Solving -4.5 + N = -6.184658438 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 = -6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + N = -6.184658438 + 4.5 N = -6.184658438 + 4.5 Combine like terms: -6.184658438 + 4.5 = -1.684658438 N = -1.684658438 Simplifying N = -1.684658438Solution
The solution to the problem is based on the solutions from the subproblems. N = {10.684658438, -1.684658438}
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