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Simplifying 6v2 + 11v + -6 = 0 Reorder the terms: -6 + 11v + 6v2 = 0 Solving -6 + 11v + 6v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + 1.833333333v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.833333333v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 1.833333333v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.833333333v + v2 = 0 + 1 1.833333333v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.833333333v + v2 = 1 The v term is 1.833333333v. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333v + 0.8402777775 + v2 = 1 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333v + v2 = 1 + 0.8402777775 Combine like terms: 1 + 0.8402777775 = 1.8402777775 0.8402777775 + 1.833333333v + v2 = 1.8402777775 Factor a perfect square on the left side: (v + 0.9166666665)(v + 0.9166666665) = 1.8402777775 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (v + 0.9166666665) equal to 1.356568383 and -1.356568383.Subproblem 1
v + 0.9166666665 = 1.356568383 Simplifying v + 0.9166666665 = 1.356568383 Reorder the terms: 0.9166666665 + v = 1.356568383 Solving 0.9166666665 + v = 1.356568383 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + v = 1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + v = 1.356568383 + -0.9166666665 v = 1.356568383 + -0.9166666665 Combine like terms: 1.356568383 + -0.9166666665 = 0.4399017165 v = 0.4399017165 Simplifying v = 0.4399017165Subproblem 2
v + 0.9166666665 = -1.356568383 Simplifying v + 0.9166666665 = -1.356568383 Reorder the terms: 0.9166666665 + v = -1.356568383 Solving 0.9166666665 + v = -1.356568383 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + v = -1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + v = -1.356568383 + -0.9166666665 v = -1.356568383 + -0.9166666665 Combine like terms: -1.356568383 + -0.9166666665 = -2.2732350495 v = -2.2732350495 Simplifying v = -2.2732350495Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.4399017165, -2.2732350495}
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