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Simplifying 7v2 + 8v + 2 = 0 Reorder the terms: 2 + 8v + 7v2 = 0 Solving 2 + 8v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 1.142857143v + v2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.142857143v + -0.2857142857 + v2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.142857143v + v2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.142857143v + v2 = 0 + -0.2857142857 1.142857143v + v2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.142857143v + v2 = -0.2857142857 The v term is 1.142857143v. 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. 1.142857143v + 0.3265306123 + v2 = -0.2857142857 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143v + v2 = -0.2857142857 + 0.3265306123 Combine like terms: -0.2857142857 + 0.3265306123 = 0.0408163266 0.3265306123 + 1.142857143v + v2 = 0.0408163266 Factor a perfect square on the left side: (v + 0.5714285715)(v + 0.5714285715) = 0.0408163266 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (v + 0.5714285715) equal to 0.202030509 and -0.202030509.Subproblem 1
v + 0.5714285715 = 0.202030509 Simplifying v + 0.5714285715 = 0.202030509 Reorder the terms: 0.5714285715 + v = 0.202030509 Solving 0.5714285715 + v = 0.202030509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + v = 0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + v = 0.202030509 + -0.5714285715 v = 0.202030509 + -0.5714285715 Combine like terms: 0.202030509 + -0.5714285715 = -0.3693980625 v = -0.3693980625 Simplifying v = -0.3693980625Subproblem 2
v + 0.5714285715 = -0.202030509 Simplifying v + 0.5714285715 = -0.202030509 Reorder the terms: 0.5714285715 + v = -0.202030509 Solving 0.5714285715 + v = -0.202030509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + v = -0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + v = -0.202030509 + -0.5714285715 v = -0.202030509 + -0.5714285715 Combine like terms: -0.202030509 + -0.5714285715 = -0.7734590805 v = -0.7734590805 Simplifying v = -0.7734590805Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.3693980625, -0.7734590805}
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