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Simplifying 3v2 + 4v + -3 = 0 Reorder the terms: -3 + 4v + 3v2 = 0 Solving -3 + 4v + 3v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 1.333333333v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.333333333v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 1.333333333v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.333333333v + v2 = 0 + 1 1.333333333v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.333333333v + v2 = 1 The v term is 1.333333333v. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333v + 0.4444444442 + v2 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333v + v2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + 1.333333333v + v2 = 1.4444444442 Factor a perfect square on the left side: (v + 0.6666666665)(v + 0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (v + 0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
v + 0.6666666665 = 1.201850425 Simplifying v + 0.6666666665 = 1.201850425 Reorder the terms: 0.6666666665 + v = 1.201850425 Solving 0.6666666665 + v = 1.201850425 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + v = 1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + v = 1.201850425 + -0.6666666665 v = 1.201850425 + -0.6666666665 Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585 v = 0.5351837585 Simplifying v = 0.5351837585Subproblem 2
v + 0.6666666665 = -1.201850425 Simplifying v + 0.6666666665 = -1.201850425 Reorder the terms: 0.6666666665 + v = -1.201850425 Solving 0.6666666665 + v = -1.201850425 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + v = -1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + v = -1.201850425 + -0.6666666665 v = -1.201850425 + -0.6666666665 Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915 v = -1.8685170915 Simplifying v = -1.8685170915Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.5351837585, -1.8685170915}
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