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Simplifying 7n2 + 5n + -360 = 0 Reorder the terms: -360 + 5n + 7n2 = 0 Solving -360 + 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'. -51.42857143 + 0.7142857143n + n2 = 0 Move the constant term to the right: Add '51.42857143' to each side of the equation. -51.42857143 + 0.7142857143n + 51.42857143 + n2 = 0 + 51.42857143 Reorder the terms: -51.42857143 + 51.42857143 + 0.7142857143n + n2 = 0 + 51.42857143 Combine like terms: -51.42857143 + 51.42857143 = 0.00000000 0.00000000 + 0.7142857143n + n2 = 0 + 51.42857143 0.7142857143n + n2 = 0 + 51.42857143 Combine like terms: 0 + 51.42857143 = 51.42857143 0.7142857143n + n2 = 51.42857143 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 = 51.42857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143n + n2 = 51.42857143 + 0.1275510204 Combine like terms: 51.42857143 + 0.1275510204 = 51.5561224504 0.1275510204 + 0.7142857143n + n2 = 51.5561224504 Factor a perfect square on the left side: (n + 0.3571428572)(n + 0.3571428572) = 51.5561224504 Calculate the square root of the right side: 7.180259219 Break this problem into two subproblems by setting (n + 0.3571428572) equal to 7.180259219 and -7.180259219.Subproblem 1
n + 0.3571428572 = 7.180259219 Simplifying n + 0.3571428572 = 7.180259219 Reorder the terms: 0.3571428572 + n = 7.180259219 Solving 0.3571428572 + n = 7.180259219 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 = 7.180259219 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + n = 7.180259219 + -0.3571428572 n = 7.180259219 + -0.3571428572 Combine like terms: 7.180259219 + -0.3571428572 = 6.8231163618 n = 6.8231163618 Simplifying n = 6.8231163618Subproblem 2
n + 0.3571428572 = -7.180259219 Simplifying n + 0.3571428572 = -7.180259219 Reorder the terms: 0.3571428572 + n = -7.180259219 Solving 0.3571428572 + n = -7.180259219 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 = -7.180259219 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + n = -7.180259219 + -0.3571428572 n = -7.180259219 + -0.3571428572 Combine like terms: -7.180259219 + -0.3571428572 = -7.5374020762 n = -7.5374020762 Simplifying n = -7.5374020762Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.8231163618, -7.5374020762}
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