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Simplifying (5n2 + -1n + 6) + (8n2 + -11) = 0 Reorder the terms: (6 + -1n + 5n2) + (8n2 + -11) = 0 Remove parenthesis around (6 + -1n + 5n2) 6 + -1n + 5n2 + (8n2 + -11) = 0 Reorder the terms: 6 + -1n + 5n2 + (-11 + 8n2) = 0 Remove parenthesis around (-11 + 8n2) 6 + -1n + 5n2 + -11 + 8n2 = 0 Reorder the terms: 6 + -11 + -1n + 5n2 + 8n2 = 0 Combine like terms: 6 + -11 = -5 -5 + -1n + 5n2 + 8n2 = 0 Combine like terms: 5n2 + 8n2 = 13n2 -5 + -1n + 13n2 = 0 Solving -5 + -1n + 13n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.3846153846 + -0.07692307692n + n2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + -0.07692307692n + 0.3846153846 + n2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + -0.07692307692n + n2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + -0.07692307692n + n2 = 0 + 0.3846153846 -0.07692307692n + n2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 -0.07692307692n + n2 = 0.3846153846 The n term is -0.07692307692n. Take half its coefficient (-0.03846153846). Square it (0.001479289941) and add it to both sides. Add '0.001479289941' to each side of the equation. -0.07692307692n + 0.001479289941 + n2 = 0.3846153846 + 0.001479289941 Reorder the terms: 0.001479289941 + -0.07692307692n + n2 = 0.3846153846 + 0.001479289941 Combine like terms: 0.3846153846 + 0.001479289941 = 0.386094674541 0.001479289941 + -0.07692307692n + n2 = 0.386094674541 Factor a perfect square on the left side: (n + -0.03846153846)(n + -0.03846153846) = 0.386094674541 Calculate the square root of the right side: 0.62136517 Break this problem into two subproblems by setting (n + -0.03846153846) equal to 0.62136517 and -0.62136517.Subproblem 1
n + -0.03846153846 = 0.62136517 Simplifying n + -0.03846153846 = 0.62136517 Reorder the terms: -0.03846153846 + n = 0.62136517 Solving -0.03846153846 + n = 0.62136517 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + n = 0.62136517 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + n = 0.62136517 + 0.03846153846 n = 0.62136517 + 0.03846153846 Combine like terms: 0.62136517 + 0.03846153846 = 0.65982670846 n = 0.65982670846 Simplifying n = 0.65982670846Subproblem 2
n + -0.03846153846 = -0.62136517 Simplifying n + -0.03846153846 = -0.62136517 Reorder the terms: -0.03846153846 + n = -0.62136517 Solving -0.03846153846 + n = -0.62136517 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + n = -0.62136517 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + n = -0.62136517 + 0.03846153846 n = -0.62136517 + 0.03846153846 Combine like terms: -0.62136517 + 0.03846153846 = -0.58290363154 n = -0.58290363154 Simplifying n = -0.58290363154Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.65982670846, -0.58290363154}
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