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Simplifying 11n2 + 6n + -21 = 0 Reorder the terms: -21 + 6n + 11n2 = 0 Solving -21 + 6n + 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'. -1.909090909 + 0.5454545455n + n2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + 0.5454545455n + 1.909090909 + n2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + 0.5454545455n + n2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + 0.5454545455n + n2 = 0 + 1.909090909 0.5454545455n + n2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 0.5454545455n + n2 = 1.909090909 The n term is 0.5454545455n. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455n + 0.07438016533 + n2 = 1.909090909 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455n + n2 = 1.909090909 + 0.07438016533 Combine like terms: 1.909090909 + 0.07438016533 = 1.98347107433 0.07438016533 + 0.5454545455n + n2 = 1.98347107433 Factor a perfect square on the left side: (n + 0.2727272728)(n + 0.2727272728) = 1.98347107433 Calculate the square root of the right side: 1.40835758 Break this problem into two subproblems by setting (n + 0.2727272728) equal to 1.40835758 and -1.40835758.Subproblem 1
n + 0.2727272728 = 1.40835758 Simplifying n + 0.2727272728 = 1.40835758 Reorder the terms: 0.2727272728 + n = 1.40835758 Solving 0.2727272728 + n = 1.40835758 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + n = 1.40835758 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + n = 1.40835758 + -0.2727272728 n = 1.40835758 + -0.2727272728 Combine like terms: 1.40835758 + -0.2727272728 = 1.1356303072 n = 1.1356303072 Simplifying n = 1.1356303072Subproblem 2
n + 0.2727272728 = -1.40835758 Simplifying n + 0.2727272728 = -1.40835758 Reorder the terms: 0.2727272728 + n = -1.40835758 Solving 0.2727272728 + n = -1.40835758 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + n = -1.40835758 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + n = -1.40835758 + -0.2727272728 n = -1.40835758 + -0.2727272728 Combine like terms: -1.40835758 + -0.2727272728 = -1.6810848528 n = -1.6810848528 Simplifying n = -1.6810848528Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.1356303072, -1.6810848528}
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