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Simplifying 11n2 + 10n + -17 = 0 Reorder the terms: -17 + 10n + 11n2 = 0 Solving -17 + 10n + 11n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.545454545 + 0.9090909091n + n2 = 0 Move the constant term to the right: Add '1.545454545' to each side of the equation. -1.545454545 + 0.9090909091n + 1.545454545 + n2 = 0 + 1.545454545 Reorder the terms: -1.545454545 + 1.545454545 + 0.9090909091n + n2 = 0 + 1.545454545 Combine like terms: -1.545454545 + 1.545454545 = 0.000000000 0.000000000 + 0.9090909091n + n2 = 0 + 1.545454545 0.9090909091n + n2 = 0 + 1.545454545 Combine like terms: 0 + 1.545454545 = 1.545454545 0.9090909091n + n2 = 1.545454545 The n term is 0.9090909091n. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091n + 0.2066115703 + n2 = 1.545454545 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091n + n2 = 1.545454545 + 0.2066115703 Combine like terms: 1.545454545 + 0.2066115703 = 1.7520661153 0.2066115703 + 0.9090909091n + n2 = 1.7520661153 Factor a perfect square on the left side: (n + 0.4545454546)(n + 0.4545454546) = 1.7520661153 Calculate the square root of the right side: 1.323656343 Break this problem into two subproblems by setting (n + 0.4545454546) equal to 1.323656343 and -1.323656343.Subproblem 1
n + 0.4545454546 = 1.323656343 Simplifying n + 0.4545454546 = 1.323656343 Reorder the terms: 0.4545454546 + n = 1.323656343 Solving 0.4545454546 + n = 1.323656343 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + n = 1.323656343 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + n = 1.323656343 + -0.4545454546 n = 1.323656343 + -0.4545454546 Combine like terms: 1.323656343 + -0.4545454546 = 0.8691108884 n = 0.8691108884 Simplifying n = 0.8691108884Subproblem 2
n + 0.4545454546 = -1.323656343 Simplifying n + 0.4545454546 = -1.323656343 Reorder the terms: 0.4545454546 + n = -1.323656343 Solving 0.4545454546 + n = -1.323656343 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + n = -1.323656343 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + n = -1.323656343 + -0.4545454546 n = -1.323656343 + -0.4545454546 Combine like terms: -1.323656343 + -0.4545454546 = -1.7782017976 n = -1.7782017976 Simplifying n = -1.7782017976Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.8691108884, -1.7782017976}
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