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Simplifying 0 = 8n2 + -64n + -1 Reorder the terms: 0 = -1 + -64n + 8n2 Solving 0 = -1 + -64n + 8n2 Solving for variable 'n'. Combine like terms: 0 + 1 = 1 1 + 64n + -8n2 = -1 + -64n + 8n2 + 1 + 64n + -8n2 Reorder the terms: 1 + 64n + -8n2 = -1 + 1 + -64n + 64n + 8n2 + -8n2 Combine like terms: -1 + 1 = 0 1 + 64n + -8n2 = 0 + -64n + 64n + 8n2 + -8n2 1 + 64n + -8n2 = -64n + 64n + 8n2 + -8n2 Combine like terms: -64n + 64n = 0 1 + 64n + -8n2 = 0 + 8n2 + -8n2 1 + 64n + -8n2 = 8n2 + -8n2 Combine like terms: 8n2 + -8n2 = 0 1 + 64n + -8n2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -8n + n2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -8n + 0.125 + n2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -8n + n2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -8n + n2 = 0 + 0.125 -8n + n2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -8n + n2 = 0.125 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 = 0.125 + 16 Reorder the terms: 16 + -8n + n2 = 0.125 + 16 Combine like terms: 0.125 + 16 = 16.125 16 + -8n + n2 = 16.125 Factor a perfect square on the left side: (n + -4)(n + -4) = 16.125 Calculate the square root of the right side: 4.015594601 Break this problem into two subproblems by setting (n + -4) equal to 4.015594601 and -4.015594601.Subproblem 1
n + -4 = 4.015594601 Simplifying n + -4 = 4.015594601 Reorder the terms: -4 + n = 4.015594601 Solving -4 + n = 4.015594601 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 = 4.015594601 + 4 Combine like terms: -4 + 4 = 0 0 + n = 4.015594601 + 4 n = 4.015594601 + 4 Combine like terms: 4.015594601 + 4 = 8.015594601 n = 8.015594601 Simplifying n = 8.015594601Subproblem 2
n + -4 = -4.015594601 Simplifying n + -4 = -4.015594601 Reorder the terms: -4 + n = -4.015594601 Solving -4 + n = -4.015594601 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 = -4.015594601 + 4 Combine like terms: -4 + 4 = 0 0 + n = -4.015594601 + 4 n = -4.015594601 + 4 Combine like terms: -4.015594601 + 4 = -0.015594601 n = -0.015594601 Simplifying n = -0.015594601Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.015594601, -0.015594601}
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