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Simplifying 11n2 + 21n + -14 = 0 Reorder the terms: -14 + 21n + 11n2 = 0 Solving -14 + 21n + 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'. -1.272727273 + 1.909090909n + n2 = 0 Move the constant term to the right: Add '1.272727273' to each side of the equation. -1.272727273 + 1.909090909n + 1.272727273 + n2 = 0 + 1.272727273 Reorder the terms: -1.272727273 + 1.272727273 + 1.909090909n + n2 = 0 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + 1.909090909n + n2 = 0 + 1.272727273 1.909090909n + n2 = 0 + 1.272727273 Combine like terms: 0 + 1.272727273 = 1.272727273 1.909090909n + n2 = 1.272727273 The n term is 1.909090909n. Take half its coefficient (0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. 1.909090909n + 0.9111570247 + n2 = 1.272727273 + 0.9111570247 Reorder the terms: 0.9111570247 + 1.909090909n + n2 = 1.272727273 + 0.9111570247 Combine like terms: 1.272727273 + 0.9111570247 = 2.1838842977 0.9111570247 + 1.909090909n + n2 = 2.1838842977 Factor a perfect square on the left side: (n + 0.9545454545)(n + 0.9545454545) = 2.1838842977 Calculate the square root of the right side: 1.47779711 Break this problem into two subproblems by setting (n + 0.9545454545) equal to 1.47779711 and -1.47779711.Subproblem 1
n + 0.9545454545 = 1.47779711 Simplifying n + 0.9545454545 = 1.47779711 Reorder the terms: 0.9545454545 + n = 1.47779711 Solving 0.9545454545 + n = 1.47779711 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.9545454545' to each side of the equation. 0.9545454545 + -0.9545454545 + n = 1.47779711 + -0.9545454545 Combine like terms: 0.9545454545 + -0.9545454545 = 0.0000000000 0.0000000000 + n = 1.47779711 + -0.9545454545 n = 1.47779711 + -0.9545454545 Combine like terms: 1.47779711 + -0.9545454545 = 0.5232516555 n = 0.5232516555 Simplifying n = 0.5232516555Subproblem 2
n + 0.9545454545 = -1.47779711 Simplifying n + 0.9545454545 = -1.47779711 Reorder the terms: 0.9545454545 + n = -1.47779711 Solving 0.9545454545 + n = -1.47779711 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.9545454545' to each side of the equation. 0.9545454545 + -0.9545454545 + n = -1.47779711 + -0.9545454545 Combine like terms: 0.9545454545 + -0.9545454545 = 0.0000000000 0.0000000000 + n = -1.47779711 + -0.9545454545 n = -1.47779711 + -0.9545454545 Combine like terms: -1.47779711 + -0.9545454545 = -2.4323425645 n = -2.4323425645 Simplifying n = -2.4323425645Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.5232516555, -2.4323425645}
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