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Simplifying -2 = -1n(n + -8) Reorder the terms: -2 = -1n(-8 + n) -2 = (-8 * -1n + n * -1n) -2 = (8n + -1n2) Solving -2 = 8n + -1n2 Solving for variable 'n'. Reorder the terms: -2 + -8n + n2 = 8n + -8n + -1n2 + n2 Combine like terms: 8n + -8n = 0 -2 + -8n + n2 = 0 + -1n2 + n2 -2 + -8n + n2 = -1n2 + n2 Combine like terms: -1n2 + n2 = 0 -2 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -8n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -8n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8n + n2 = 0 + 2 -8n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8n + n2 = 2 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 = 2 + 16 Reorder the terms: 16 + -8n + n2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + -8n + n2 = 18 Factor a perfect square on the left side: (n + -4)(n + -4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (n + -4) equal to 4.242640687 and -4.242640687.Subproblem 1
n + -4 = 4.242640687 Simplifying n + -4 = 4.242640687 Reorder the terms: -4 + n = 4.242640687 Solving -4 + n = 4.242640687 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 = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + n = 4.242640687 + 4 n = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 n = 8.242640687 Simplifying n = 8.242640687Subproblem 2
n + -4 = -4.242640687 Simplifying n + -4 = -4.242640687 Reorder the terms: -4 + n = -4.242640687 Solving -4 + n = -4.242640687 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 = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + n = -4.242640687 + 4 n = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 n = -0.242640687 Simplifying n = -0.242640687Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.242640687, -0.242640687}
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