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Simplifying 2n2 + 11n + 2 = 0 Reorder the terms: 2 + 11n + 2n2 = 0 Solving 2 + 11n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 5.5n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5.5n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + 5.5n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5.5n + n2 = 0 + -1 5.5n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 5.5n + n2 = -1 The n term is 5.5n. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5n + 7.5625 + n2 = -1 + 7.5625 Reorder the terms: 7.5625 + 5.5n + n2 = -1 + 7.5625 Combine like terms: -1 + 7.5625 = 6.5625 7.5625 + 5.5n + n2 = 6.5625 Factor a perfect square on the left side: (n + 2.75)(n + 2.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (n + 2.75) equal to 2.561737691 and -2.561737691.Subproblem 1
n + 2.75 = 2.561737691 Simplifying n + 2.75 = 2.561737691 Reorder the terms: 2.75 + n = 2.561737691 Solving 2.75 + n = 2.561737691 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + n = 2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + n = 2.561737691 + -2.75 n = 2.561737691 + -2.75 Combine like terms: 2.561737691 + -2.75 = -0.188262309 n = -0.188262309 Simplifying n = -0.188262309Subproblem 2
n + 2.75 = -2.561737691 Simplifying n + 2.75 = -2.561737691 Reorder the terms: 2.75 + n = -2.561737691 Solving 2.75 + n = -2.561737691 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + n = -2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + n = -2.561737691 + -2.75 n = -2.561737691 + -2.75 Combine like terms: -2.561737691 + -2.75 = -5.311737691 n = -5.311737691 Simplifying n = -5.311737691Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.188262309, -5.311737691}
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