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Simplifying 11v2 + 11v + 2 = 0 Reorder the terms: 2 + 11v + 11v2 = 0 Solving 2 + 11v + 11v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + v + v2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + v + -0.1818181818 + v2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + v + v2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + v + v2 = 0 + -0.1818181818 v + v2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 v + v2 = -0.1818181818 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = -0.1818181818 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = -0.1818181818 + 0.25 Combine like terms: -0.1818181818 + 0.25 = 0.0681818182 1.25 + v2 = 0.0681818182 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 0.0681818182 Calculate the square root of the right side: 0.261116484 Break this problem into two subproblems by setting (v + 0.5) equal to 0.261116484 and -0.261116484.Subproblem 1
v + 0.5 = 0.261116484 Simplifying v + 0.5 = 0.261116484 Reorder the terms: 0.5 + v = 0.261116484 Solving 0.5 + v = 0.261116484 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 0.261116484 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 0.261116484 + -0.5 v = 0.261116484 + -0.5 Combine like terms: 0.261116484 + -0.5 = -0.238883516 v = -0.238883516 Simplifying v = -0.238883516Subproblem 2
v + 0.5 = -0.261116484 Simplifying v + 0.5 = -0.261116484 Reorder the terms: 0.5 + v = -0.261116484 Solving 0.5 + v = -0.261116484 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -0.261116484 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -0.261116484 + -0.5 v = -0.261116484 + -0.5 Combine like terms: -0.261116484 + -0.5 = -0.761116484 v = -0.761116484 Simplifying v = -0.761116484Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.238883516, -0.761116484}
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