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Simplifying 7n2 + 117n + -1350 = 0 Reorder the terms: -1350 + 117n + 7n2 = 0 Solving -1350 + 117n + 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'. -192.8571429 + 16.71428571n + n2 = 0 Move the constant term to the right: Add '192.8571429' to each side of the equation. -192.8571429 + 16.71428571n + 192.8571429 + n2 = 0 + 192.8571429 Reorder the terms: -192.8571429 + 192.8571429 + 16.71428571n + n2 = 0 + 192.8571429 Combine like terms: -192.8571429 + 192.8571429 = 0.0000000 0.0000000 + 16.71428571n + n2 = 0 + 192.8571429 16.71428571n + n2 = 0 + 192.8571429 Combine like terms: 0 + 192.8571429 = 192.8571429 16.71428571n + n2 = 192.8571429 The n term is 16.71428571n. Take half its coefficient (8.357142855). Square it (69.84183670) and add it to both sides. Add '69.84183670' to each side of the equation. 16.71428571n + 69.84183670 + n2 = 192.8571429 + 69.84183670 Reorder the terms: 69.84183670 + 16.71428571n + n2 = 192.8571429 + 69.84183670 Combine like terms: 192.8571429 + 69.84183670 = 262.6989796 69.84183670 + 16.71428571n + n2 = 262.6989796 Factor a perfect square on the left side: (n + 8.357142855)(n + 8.357142855) = 262.6989796 Calculate the square root of the right side: 16.207991227 Break this problem into two subproblems by setting (n + 8.357142855) equal to 16.207991227 and -16.207991227.Subproblem 1
n + 8.357142855 = 16.207991227 Simplifying n + 8.357142855 = 16.207991227 Reorder the terms: 8.357142855 + n = 16.207991227 Solving 8.357142855 + n = 16.207991227 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8.357142855' to each side of the equation. 8.357142855 + -8.357142855 + n = 16.207991227 + -8.357142855 Combine like terms: 8.357142855 + -8.357142855 = 0.000000000 0.000000000 + n = 16.207991227 + -8.357142855 n = 16.207991227 + -8.357142855 Combine like terms: 16.207991227 + -8.357142855 = 7.850848372 n = 7.850848372 Simplifying n = 7.850848372Subproblem 2
n + 8.357142855 = -16.207991227 Simplifying n + 8.357142855 = -16.207991227 Reorder the terms: 8.357142855 + n = -16.207991227 Solving 8.357142855 + n = -16.207991227 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8.357142855' to each side of the equation. 8.357142855 + -8.357142855 + n = -16.207991227 + -8.357142855 Combine like terms: 8.357142855 + -8.357142855 = 0.000000000 0.000000000 + n = -16.207991227 + -8.357142855 n = -16.207991227 + -8.357142855 Combine like terms: -16.207991227 + -8.357142855 = -24.565134082 n = -24.565134082 Simplifying n = -24.565134082Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.850848372, -24.565134082}
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