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Simplifying 7n2 = -8n + -2 Reorder the terms: 7n2 = -2 + -8n Solving 7n2 = -2 + -8n Solving for variable 'n'. Reorder the terms: 2 + 8n + 7n2 = -2 + -8n + 2 + 8n Reorder the terms: 2 + 8n + 7n2 = -2 + 2 + -8n + 8n Combine like terms: -2 + 2 = 0 2 + 8n + 7n2 = 0 + -8n + 8n 2 + 8n + 7n2 = -8n + 8n Combine like terms: -8n + 8n = 0 2 + 8n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 1.142857143n + n2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.142857143n + -0.2857142857 + n2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.142857143n + n2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.142857143n + n2 = 0 + -0.2857142857 1.142857143n + n2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.142857143n + n2 = -0.2857142857 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 = -0.2857142857 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143n + n2 = -0.2857142857 + 0.3265306123 Combine like terms: -0.2857142857 + 0.3265306123 = 0.0408163266 0.3265306123 + 1.142857143n + n2 = 0.0408163266 Factor a perfect square on the left side: (n + 0.5714285715)(n + 0.5714285715) = 0.0408163266 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (n + 0.5714285715) equal to 0.202030509 and -0.202030509.Subproblem 1
n + 0.5714285715 = 0.202030509 Simplifying n + 0.5714285715 = 0.202030509 Reorder the terms: 0.5714285715 + n = 0.202030509 Solving 0.5714285715 + n = 0.202030509 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 = 0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + n = 0.202030509 + -0.5714285715 n = 0.202030509 + -0.5714285715 Combine like terms: 0.202030509 + -0.5714285715 = -0.3693980625 n = -0.3693980625 Simplifying n = -0.3693980625Subproblem 2
n + 0.5714285715 = -0.202030509 Simplifying n + 0.5714285715 = -0.202030509 Reorder the terms: 0.5714285715 + n = -0.202030509 Solving 0.5714285715 + n = -0.202030509 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 = -0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + n = -0.202030509 + -0.5714285715 n = -0.202030509 + -0.5714285715 Combine like terms: -0.202030509 + -0.5714285715 = -0.7734590805 n = -0.7734590805 Simplifying n = -0.7734590805Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.3693980625, -0.7734590805}
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