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Simplifying 7n2 + 26n + -18150 = 0 Reorder the terms: -18150 + 26n + 7n2 = 0 Solving -18150 + 26n + 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'. -2592.857143 + 3.714285714n + n2 = 0 Move the constant term to the right: Add '2592.857143' to each side of the equation. -2592.857143 + 3.714285714n + 2592.857143 + n2 = 0 + 2592.857143 Reorder the terms: -2592.857143 + 2592.857143 + 3.714285714n + n2 = 0 + 2592.857143 Combine like terms: -2592.857143 + 2592.857143 = 0.000000 0.000000 + 3.714285714n + n2 = 0 + 2592.857143 3.714285714n + n2 = 0 + 2592.857143 Combine like terms: 0 + 2592.857143 = 2592.857143 3.714285714n + n2 = 2592.857143 The n term is 3.714285714n. Take half its coefficient (1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. 3.714285714n + 3.448979591 + n2 = 2592.857143 + 3.448979591 Reorder the terms: 3.448979591 + 3.714285714n + n2 = 2592.857143 + 3.448979591 Combine like terms: 2592.857143 + 3.448979591 = 2596.306122591 3.448979591 + 3.714285714n + n2 = 2596.306122591 Factor a perfect square on the left side: (n + 1.857142857)(n + 1.857142857) = 2596.306122591 Calculate the square root of the right side: 50.953960814 Break this problem into two subproblems by setting (n + 1.857142857) equal to 50.953960814 and -50.953960814.Subproblem 1
n + 1.857142857 = 50.953960814 Simplifying n + 1.857142857 = 50.953960814 Reorder the terms: 1.857142857 + n = 50.953960814 Solving 1.857142857 + n = 50.953960814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + n = 50.953960814 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + n = 50.953960814 + -1.857142857 n = 50.953960814 + -1.857142857 Combine like terms: 50.953960814 + -1.857142857 = 49.096817957 n = 49.096817957 Simplifying n = 49.096817957Subproblem 2
n + 1.857142857 = -50.953960814 Simplifying n + 1.857142857 = -50.953960814 Reorder the terms: 1.857142857 + n = -50.953960814 Solving 1.857142857 + n = -50.953960814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + n = -50.953960814 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + n = -50.953960814 + -1.857142857 n = -50.953960814 + -1.857142857 Combine like terms: -50.953960814 + -1.857142857 = -52.811103671 n = -52.811103671 Simplifying n = -52.811103671Solution
The solution to the problem is based on the solutions from the subproblems. n = {49.096817957, -52.811103671}
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