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Simplifying (4v2 + -3v + -7) + (2v2 + -5v + 1) = 0 Reorder the terms: (-7 + -3v + 4v2) + (2v2 + -5v + 1) = 0 Remove parenthesis around (-7 + -3v + 4v2) -7 + -3v + 4v2 + (2v2 + -5v + 1) = 0 Reorder the terms: -7 + -3v + 4v2 + (1 + -5v + 2v2) = 0 Remove parenthesis around (1 + -5v + 2v2) -7 + -3v + 4v2 + 1 + -5v + 2v2 = 0 Reorder the terms: -7 + 1 + -3v + -5v + 4v2 + 2v2 = 0 Combine like terms: -7 + 1 = -6 -6 + -3v + -5v + 4v2 + 2v2 = 0 Combine like terms: -3v + -5v = -8v -6 + -8v + 4v2 + 2v2 = 0 Combine like terms: 4v2 + 2v2 = 6v2 -6 + -8v + 6v2 = 0 Solving -6 + -8v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -4v + 3v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4v + 3v2)' equal to zero and attempt to solve: Simplifying -3 + -4v + 3v2 = 0 Solving -3 + -4v + 3v2 = 0 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 = 1.8685170915 v = 1.8685170915 Simplifying v = 1.8685170915Subproblem 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 = -0.5351837585 v = -0.5351837585 Simplifying v = -0.5351837585Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.8685170915, -0.5351837585}Solution
v = {1.8685170915, -0.5351837585}
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