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Simplifying 8n(n + -2) = 5 Reorder the terms: 8n(-2 + n) = 5 (-2 * 8n + n * 8n) = 5 (-16n + 8n2) = 5 Solving -16n + 8n2 = 5 Solving for variable 'n'. Reorder the terms: -5 + -16n + 8n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -16n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -2n + n2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2n + 0.625 + n2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2n + n2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2n + n2 = 0 + 0.625 -2n + n2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2n + n2 = 0.625 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 0.625 + 1 Reorder the terms: 1 + -2n + n2 = 0.625 + 1 Combine like terms: 0.625 + 1 = 1.625 1 + -2n + n2 = 1.625 Factor a perfect square on the left side: (n + -1)(n + -1) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (n + -1) equal to 1.274754878 and -1.274754878.Subproblem 1
n + -1 = 1.274754878 Simplifying n + -1 = 1.274754878 Reorder the terms: -1 + n = 1.274754878 Solving -1 + n = 1.274754878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.274754878 + 1 n = 1.274754878 + 1 Combine like terms: 1.274754878 + 1 = 2.274754878 n = 2.274754878 Simplifying n = 2.274754878Subproblem 2
n + -1 = -1.274754878 Simplifying n + -1 = -1.274754878 Reorder the terms: -1 + n = -1.274754878 Solving -1 + n = -1.274754878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.274754878 + 1 n = -1.274754878 + 1 Combine like terms: -1.274754878 + 1 = -0.274754878 n = -0.274754878 Simplifying n = -0.274754878Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.274754878, -0.274754878}
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