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Simplifying 11n2 = -8n + 17 Reorder the terms: 11n2 = 17 + -8n Solving 11n2 = 17 + -8n Solving for variable 'n'. Reorder the terms: -17 + 8n + 11n2 = 17 + -8n + -17 + 8n Reorder the terms: -17 + 8n + 11n2 = 17 + -17 + -8n + 8n Combine like terms: 17 + -17 = 0 -17 + 8n + 11n2 = 0 + -8n + 8n -17 + 8n + 11n2 = -8n + 8n Combine like terms: -8n + 8n = 0 -17 + 8n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.545454545 + 0.7272727273n + n2 = 0 Move the constant term to the right: Add '1.545454545' to each side of the equation. -1.545454545 + 0.7272727273n + 1.545454545 + n2 = 0 + 1.545454545 Reorder the terms: -1.545454545 + 1.545454545 + 0.7272727273n + n2 = 0 + 1.545454545 Combine like terms: -1.545454545 + 1.545454545 = 0.000000000 0.000000000 + 0.7272727273n + n2 = 0 + 1.545454545 0.7272727273n + n2 = 0 + 1.545454545 Combine like terms: 0 + 1.545454545 = 1.545454545 0.7272727273n + n2 = 1.545454545 The n term is 0.7272727273n. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273n + 0.1322314050 + n2 = 1.545454545 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273n + n2 = 1.545454545 + 0.1322314050 Combine like terms: 1.545454545 + 0.1322314050 = 1.67768595 0.1322314050 + 0.7272727273n + n2 = 1.67768595 Factor a perfect square on the left side: (n + 0.3636363637)(n + 0.3636363637) = 1.67768595 Calculate the square root of the right side: 1.295255168 Break this problem into two subproblems by setting (n + 0.3636363637) equal to 1.295255168 and -1.295255168.Subproblem 1
n + 0.3636363637 = 1.295255168 Simplifying n + 0.3636363637 = 1.295255168 Reorder the terms: 0.3636363637 + n = 1.295255168 Solving 0.3636363637 + n = 1.295255168 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + n = 1.295255168 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + n = 1.295255168 + -0.3636363637 n = 1.295255168 + -0.3636363637 Combine like terms: 1.295255168 + -0.3636363637 = 0.9316188043 n = 0.9316188043 Simplifying n = 0.9316188043Subproblem 2
n + 0.3636363637 = -1.295255168 Simplifying n + 0.3636363637 = -1.295255168 Reorder the terms: 0.3636363637 + n = -1.295255168 Solving 0.3636363637 + n = -1.295255168 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + n = -1.295255168 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + n = -1.295255168 + -0.3636363637 n = -1.295255168 + -0.3636363637 Combine like terms: -1.295255168 + -0.3636363637 = -1.6588915317 n = -1.6588915317 Simplifying n = -1.6588915317Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.9316188043, -1.6588915317}
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