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Simplifying 3N(N + -12) = 36 Reorder the terms: 3N(-12 + N) = 36 (-12 * 3N + N * 3N) = 36 (-36N + 3N2) = 36 Solving -36N + 3N2 = 36 Solving for variable 'N'. Reorder the terms: -36 + -36N + 3N2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -36N + 3N2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -12N + N2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + -12N + N2)' equal to zero and attempt to solve: Simplifying -12 + -12N + N2 = 0 Solving -12 + -12N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -12N + 12 + N2 = 0 + 12 Reorder the terms: -12 + 12 + -12N + N2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -12N + N2 = 0 + 12 -12N + N2 = 0 + 12 Combine like terms: 0 + 12 = 12 -12N + N2 = 12 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 = 12 + 36 Reorder the terms: 36 + -12N + N2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + -12N + N2 = 48 Factor a perfect square on the left side: (N + -6)(N + -6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (N + -6) equal to 6.92820323 and -6.92820323.Subproblem 1
N + -6 = 6.92820323 Simplifying N + -6 = 6.92820323 Reorder the terms: -6 + N = 6.92820323 Solving -6 + N = 6.92820323 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 = 6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + N = 6.92820323 + 6 N = 6.92820323 + 6 Combine like terms: 6.92820323 + 6 = 12.92820323 N = 12.92820323 Simplifying N = 12.92820323Subproblem 2
N + -6 = -6.92820323 Simplifying N + -6 = -6.92820323 Reorder the terms: -6 + N = -6.92820323 Solving -6 + N = -6.92820323 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 = -6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + N = -6.92820323 + 6 N = -6.92820323 + 6 Combine like terms: -6.92820323 + 6 = -0.92820323 N = -0.92820323 Simplifying N = -0.92820323Solution
The solution to the problem is based on the solutions from the subproblems. N = {12.92820323, -0.92820323}Solution
N = {12.92820323, -0.92820323}
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