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Simplifying (2n2 + -5n + -6) + (-1n2 + -3n + 11) = 0 Reorder the terms: (-6 + -5n + 2n2) + (-1n2 + -3n + 11) = 0 Remove parenthesis around (-6 + -5n + 2n2) -6 + -5n + 2n2 + (-1n2 + -3n + 11) = 0 Reorder the terms: -6 + -5n + 2n2 + (11 + -3n + -1n2) = 0 Remove parenthesis around (11 + -3n + -1n2) -6 + -5n + 2n2 + 11 + -3n + -1n2 = 0 Reorder the terms: -6 + 11 + -5n + -3n + 2n2 + -1n2 = 0 Combine like terms: -6 + 11 = 5 5 + -5n + -3n + 2n2 + -1n2 = 0 Combine like terms: -5n + -3n = -8n 5 + -8n + 2n2 + -1n2 = 0 Combine like terms: 2n2 + -1n2 = 1n2 5 + -8n + 1n2 = 0 Solving 5 + -8n + 1n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + -8n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8n + n2 = 0 + -5 -8n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8n + n2 = -5 The n term is -8n. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8n + 16 + n2 = -5 + 16 Reorder the terms: 16 + -8n + n2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8n + n2 = 11 Factor a perfect square on the left side: (n + -4)(n + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
n + -4 = 3.31662479 Simplifying n + -4 = 3.31662479 Reorder the terms: -4 + n = 3.31662479 Solving -4 + n = 3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + n = 3.31662479 + 4 n = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 n = 7.31662479 Simplifying n = 7.31662479Subproblem 2
n + -4 = -3.31662479 Simplifying n + -4 = -3.31662479 Reorder the terms: -4 + n = -3.31662479 Solving -4 + n = -3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + n = -3.31662479 + 4 n = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 n = 0.68337521 Simplifying n = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.31662479, 0.68337521}
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