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Simplifying (-5v2 + v + -3) + (4v2 + 6v + 2) = 0 Reorder the terms: (-3 + v + -5v2) + (4v2 + 6v + 2) = 0 Remove parenthesis around (-3 + v + -5v2) -3 + v + -5v2 + (4v2 + 6v + 2) = 0 Reorder the terms: -3 + v + -5v2 + (2 + 6v + 4v2) = 0 Remove parenthesis around (2 + 6v + 4v2) -3 + v + -5v2 + 2 + 6v + 4v2 = 0 Reorder the terms: -3 + 2 + v + 6v + -5v2 + 4v2 = 0 Combine like terms: -3 + 2 = -1 -1 + v + 6v + -5v2 + 4v2 = 0 Combine like terms: v + 6v = 7v -1 + 7v + -5v2 + 4v2 = 0 Combine like terms: -5v2 + 4v2 = -1v2 -1 + 7v + -1v2 = 0 Solving -1 + 7v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -7v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -7v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7v + v2 = 0 + -1 -7v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7v + v2 = -1 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = -1 + 12.25 Reorder the terms: 12.25 + -7v + v2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + -7v + v2 = 11.25 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (v + -3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
v + -3.5 = 3.354101966 Simplifying v + -3.5 = 3.354101966 Reorder the terms: -3.5 + v = 3.354101966 Solving -3.5 + v = 3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 3.354101966 + 3.5 v = 3.354101966 + 3.5 Combine like terms: 3.354101966 + 3.5 = 6.854101966 v = 6.854101966 Simplifying v = 6.854101966Subproblem 2
v + -3.5 = -3.354101966 Simplifying v + -3.5 = -3.354101966 Reorder the terms: -3.5 + v = -3.354101966 Solving -3.5 + v = -3.354101966 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -3.354101966 + 3.5 v = -3.354101966 + 3.5 Combine like terms: -3.354101966 + 3.5 = 0.145898034 v = 0.145898034 Simplifying v = 0.145898034Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.854101966, 0.145898034}
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