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Simplifying 11v2 + 6v + -13 = 0 Reorder the terms: -13 + 6v + 11v2 = 0 Solving -13 + 6v + 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'. -1.181818182 + 0.5454545455v + v2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + 0.5454545455v + 1.181818182 + v2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + 0.5454545455v + v2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + 0.5454545455v + v2 = 0 + 1.181818182 0.5454545455v + v2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 0.5454545455v + v2 = 1.181818182 The v term is 0.5454545455v. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455v + 0.07438016533 + v2 = 1.181818182 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455v + v2 = 1.181818182 + 0.07438016533 Combine like terms: 1.181818182 + 0.07438016533 = 1.25619834733 0.07438016533 + 0.5454545455v + v2 = 1.25619834733 Factor a perfect square on the left side: (v + 0.2727272728)(v + 0.2727272728) = 1.25619834733 Calculate the square root of the right side: 1.120802546 Break this problem into two subproblems by setting (v + 0.2727272728) equal to 1.120802546 and -1.120802546.Subproblem 1
v + 0.2727272728 = 1.120802546 Simplifying v + 0.2727272728 = 1.120802546 Reorder the terms: 0.2727272728 + v = 1.120802546 Solving 0.2727272728 + v = 1.120802546 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + v = 1.120802546 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + v = 1.120802546 + -0.2727272728 v = 1.120802546 + -0.2727272728 Combine like terms: 1.120802546 + -0.2727272728 = 0.8480752732 v = 0.8480752732 Simplifying v = 0.8480752732Subproblem 2
v + 0.2727272728 = -1.120802546 Simplifying v + 0.2727272728 = -1.120802546 Reorder the terms: 0.2727272728 + v = -1.120802546 Solving 0.2727272728 + v = -1.120802546 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + v = -1.120802546 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + v = -1.120802546 + -0.2727272728 v = -1.120802546 + -0.2727272728 Combine like terms: -1.120802546 + -0.2727272728 = -1.3935298188 v = -1.3935298188 Simplifying v = -1.3935298188Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.8480752732, -1.3935298188}
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