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Simplifying 7n2 + 8n + -6 = 0 Reorder the terms: -6 + 8n + 7n2 = 0 Solving -6 + 8n + 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'. -0.8571428571 + 1.142857143n + n2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 1.142857143n + 0.8571428571 + n2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 1.142857143n + n2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 1.142857143n + n2 = 0 + 0.8571428571 1.142857143n + n2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 1.142857143n + n2 = 0.8571428571 The n term is 1.142857143n. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143n + 0.3265306123 + n2 = 0.8571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143n + n2 = 0.8571428571 + 0.3265306123 Combine like terms: 0.8571428571 + 0.3265306123 = 1.1836734694 0.3265306123 + 1.142857143n + n2 = 1.1836734694 Factor a perfect square on the left side: (n + 0.5714285715)(n + 0.5714285715) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (n + 0.5714285715) equal to 1.087967587 and -1.087967587.Subproblem 1
n + 0.5714285715 = 1.087967587 Simplifying n + 0.5714285715 = 1.087967587 Reorder the terms: 0.5714285715 + n = 1.087967587 Solving 0.5714285715 + n = 1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + n = 1.087967587 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + n = 1.087967587 + -0.5714285715 n = 1.087967587 + -0.5714285715 Combine like terms: 1.087967587 + -0.5714285715 = 0.5165390155 n = 0.5165390155 Simplifying n = 0.5165390155Subproblem 2
n + 0.5714285715 = -1.087967587 Simplifying n + 0.5714285715 = -1.087967587 Reorder the terms: 0.5714285715 + n = -1.087967587 Solving 0.5714285715 + n = -1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + n = -1.087967587 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + n = -1.087967587 + -0.5714285715 n = -1.087967587 + -0.5714285715 Combine like terms: -1.087967587 + -0.5714285715 = -1.6593961585 n = -1.6593961585 Simplifying n = -1.6593961585Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.5165390155, -1.6593961585}
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