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Simplifying N2 + -12N + -36 = 0 Reorder the terms: -36 + -12N + N2 = 0 Solving -36 + -12N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -12N + 36 + N2 = 0 + 36 Reorder the terms: -36 + 36 + -12N + N2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12N + N2 = 0 + 36 -12N + N2 = 0 + 36 Combine like terms: 0 + 36 = 36 -12N + N2 = 36 The N term is -12N. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12N + 36 + N2 = 36 + 36 Reorder the terms: 36 + -12N + N2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + -12N + N2 = 72 Factor a perfect square on the left side: (N + -6)(N + -6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (N + -6) equal to 8.485281374 and -8.485281374.Subproblem 1
N + -6 = 8.485281374 Simplifying N + -6 = 8.485281374 Reorder the terms: -6 + N = 8.485281374 Solving -6 + N = 8.485281374 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + N = 8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + N = 8.485281374 + 6 N = 8.485281374 + 6 Combine like terms: 8.485281374 + 6 = 14.485281374 N = 14.485281374 Simplifying N = 14.485281374Subproblem 2
N + -6 = -8.485281374 Simplifying N + -6 = -8.485281374 Reorder the terms: -6 + N = -8.485281374 Solving -6 + N = -8.485281374 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + N = -8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + N = -8.485281374 + 6 N = -8.485281374 + 6 Combine like terms: -8.485281374 + 6 = -2.485281374 N = -2.485281374 Simplifying N = -2.485281374Solution
The solution to the problem is based on the solutions from the subproblems. N = {14.485281374, -2.485281374}
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