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Simplifying 8n2 + -1n + -8 = 11 Reorder the terms: -8 + -1n + 8n2 = 11 Solving -8 + -1n + 8n2 = 11 Solving for variable 'n'. Reorder the terms: -8 + -11 + -1n + 8n2 = 11 + -11 Combine like terms: -8 + -11 = -19 -19 + -1n + 8n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -19 + -1n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + -0.125n + n2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -0.125n + 2.375 + n2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -0.125n + n2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -0.125n + n2 = 0 + 2.375 -0.125n + n2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -0.125n + n2 = 2.375 The n term is -0.125n. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125n + 0.00390625 + n2 = 2.375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125n + n2 = 2.375 + 0.00390625 Combine like terms: 2.375 + 0.00390625 = 2.37890625 0.00390625 + -0.125n + n2 = 2.37890625 Factor a perfect square on the left side: (n + -0.0625)(n + -0.0625) = 2.37890625 Calculate the square root of the right side: 1.542370335 Break this problem into two subproblems by setting (n + -0.0625) equal to 1.542370335 and -1.542370335.Subproblem 1
n + -0.0625 = 1.542370335 Simplifying n + -0.0625 = 1.542370335 Reorder the terms: -0.0625 + n = 1.542370335 Solving -0.0625 + n = 1.542370335 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + n = 1.542370335 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + n = 1.542370335 + 0.0625 n = 1.542370335 + 0.0625 Combine like terms: 1.542370335 + 0.0625 = 1.604870335 n = 1.604870335 Simplifying n = 1.604870335Subproblem 2
n + -0.0625 = -1.542370335 Simplifying n + -0.0625 = -1.542370335 Reorder the terms: -0.0625 + n = -1.542370335 Solving -0.0625 + n = -1.542370335 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + n = -1.542370335 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + n = -1.542370335 + 0.0625 n = -1.542370335 + 0.0625 Combine like terms: -1.542370335 + 0.0625 = -1.479870335 n = -1.479870335 Simplifying n = -1.479870335Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.604870335, -1.479870335}
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