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Simplifying (5v2 + -7v + -1) + (6v2 + -4v + 2) = 0 Reorder the terms: (-1 + -7v + 5v2) + (6v2 + -4v + 2) = 0 Remove parenthesis around (-1 + -7v + 5v2) -1 + -7v + 5v2 + (6v2 + -4v + 2) = 0 Reorder the terms: -1 + -7v + 5v2 + (2 + -4v + 6v2) = 0 Remove parenthesis around (2 + -4v + 6v2) -1 + -7v + 5v2 + 2 + -4v + 6v2 = 0 Reorder the terms: -1 + 2 + -7v + -4v + 5v2 + 6v2 = 0 Combine like terms: -1 + 2 = 1 1 + -7v + -4v + 5v2 + 6v2 = 0 Combine like terms: -7v + -4v = -11v 1 + -11v + 5v2 + 6v2 = 0 Combine like terms: 5v2 + 6v2 = 11v2 1 + -11v + 11v2 = 0 Solving 1 + -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'. 0.09090909091 + -1v + v2 = 0 Move the constant term to the right: Add '-0.09090909091' to each side of the equation. 0.09090909091 + -1v + -0.09090909091 + v2 = 0 + -0.09090909091 Reorder the terms: 0.09090909091 + -0.09090909091 + -1v + v2 = 0 + -0.09090909091 Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000 0.00000000000 + -1v + v2 = 0 + -0.09090909091 -1v + v2 = 0 + -0.09090909091 Combine like terms: 0 + -0.09090909091 = -0.09090909091 -1v + v2 = -0.09090909091 The v term is -1v. 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. -1v + 0.25 + v2 = -0.09090909091 + 0.25 Reorder the terms: 0.25 + -1v + v2 = -0.09090909091 + 0.25 Combine like terms: -0.09090909091 + 0.25 = 0.15909090909 0.25 + -1v + v2 = 0.15909090909 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 0.15909090909 Calculate the square root of the right side: 0.398862018 Break this problem into two subproblems by setting (v + -0.5) equal to 0.398862018 and -0.398862018.Subproblem 1
v + -0.5 = 0.398862018 Simplifying v + -0.5 = 0.398862018 Reorder the terms: -0.5 + v = 0.398862018 Solving -0.5 + v = 0.398862018 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 = 0.398862018 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 0.398862018 + 0.5 v = 0.398862018 + 0.5 Combine like terms: 0.398862018 + 0.5 = 0.898862018 v = 0.898862018 Simplifying v = 0.898862018Subproblem 2
v + -0.5 = -0.398862018 Simplifying v + -0.5 = -0.398862018 Reorder the terms: -0.5 + v = -0.398862018 Solving -0.5 + v = -0.398862018 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 = -0.398862018 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -0.398862018 + 0.5 v = -0.398862018 + 0.5 Combine like terms: -0.398862018 + 0.5 = 0.101137982 v = 0.101137982 Simplifying v = 0.101137982Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.898862018, 0.101137982}
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