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Simplifying 7n2 + 5n + -8 = 0 Reorder the terms: -8 + 5n + 7n2 = 0 Solving -8 + 5n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 0.7142857143n + n2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.7142857143n + 1.142857143 + n2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.7142857143n + n2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.7142857143n + n2 = 0 + 1.142857143 0.7142857143n + n2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.7142857143n + n2 = 1.142857143 The n term is 0.7142857143n. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143n + 0.1275510204 + n2 = 1.142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143n + n2 = 1.142857143 + 0.1275510204 Combine like terms: 1.142857143 + 0.1275510204 = 1.2704081634 0.1275510204 + 0.7142857143n + n2 = 1.2704081634 Factor a perfect square on the left side: (n + 0.3571428572)(n + 0.3571428572) = 1.2704081634 Calculate the square root of the right side: 1.127123846 Break this problem into two subproblems by setting (n + 0.3571428572) equal to 1.127123846 and -1.127123846.Subproblem 1
n + 0.3571428572 = 1.127123846 Simplifying n + 0.3571428572 = 1.127123846 Reorder the terms: 0.3571428572 + n = 1.127123846 Solving 0.3571428572 + n = 1.127123846 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + n = 1.127123846 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + n = 1.127123846 + -0.3571428572 n = 1.127123846 + -0.3571428572 Combine like terms: 1.127123846 + -0.3571428572 = 0.7699809888 n = 0.7699809888 Simplifying n = 0.7699809888Subproblem 2
n + 0.3571428572 = -1.127123846 Simplifying n + 0.3571428572 = -1.127123846 Reorder the terms: 0.3571428572 + n = -1.127123846 Solving 0.3571428572 + n = -1.127123846 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + n = -1.127123846 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + n = -1.127123846 + -0.3571428572 n = -1.127123846 + -0.3571428572 Combine like terms: -1.127123846 + -0.3571428572 = -1.4842667032 n = -1.4842667032 Simplifying n = -1.4842667032Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.7699809888, -1.4842667032}
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