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Simplifying -2v2 + -1v + 2 = 3v2 + 6v Reorder the terms: 2 + -1v + -2v2 = 3v2 + 6v Reorder the terms: 2 + -1v + -2v2 = 6v + 3v2 Solving 2 + -1v + -2v2 = 6v + 3v2 Solving for variable 'v'. Reorder the terms: 2 + -1v + -6v + -2v2 + -3v2 = 6v + 3v2 + -6v + -3v2 Combine like terms: -1v + -6v = -7v 2 + -7v + -2v2 + -3v2 = 6v + 3v2 + -6v + -3v2 Combine like terms: -2v2 + -3v2 = -5v2 2 + -7v + -5v2 = 6v + 3v2 + -6v + -3v2 Reorder the terms: 2 + -7v + -5v2 = 6v + -6v + 3v2 + -3v2 Combine like terms: 6v + -6v = 0 2 + -7v + -5v2 = 0 + 3v2 + -3v2 2 + -7v + -5v2 = 3v2 + -3v2 Combine like terms: 3v2 + -3v2 = 0 2 + -7v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + 1.4v + v2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.4v + 0.4 + v2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.4v + v2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.4v + v2 = 0 + 0.4 1.4v + v2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.4v + v2 = 0.4 The v term is 1.4v. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4v + 0.49 + v2 = 0.4 + 0.49 Reorder the terms: 0.49 + 1.4v + v2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + 1.4v + v2 = 0.89 Factor a perfect square on the left side: (v + 0.7)(v + 0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (v + 0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
v + 0.7 = 0.943398113 Simplifying v + 0.7 = 0.943398113 Reorder the terms: 0.7 + v = 0.943398113 Solving 0.7 + v = 0.943398113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + v = 0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + v = 0.943398113 + -0.7 v = 0.943398113 + -0.7 Combine like terms: 0.943398113 + -0.7 = 0.243398113 v = 0.243398113 Simplifying v = 0.243398113Subproblem 2
v + 0.7 = -0.943398113 Simplifying v + 0.7 = -0.943398113 Reorder the terms: 0.7 + v = -0.943398113 Solving 0.7 + v = -0.943398113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + v = -0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + v = -0.943398113 + -0.7 v = -0.943398113 + -0.7 Combine like terms: -0.943398113 + -0.7 = -1.643398113 v = -1.643398113 Simplifying v = -1.643398113Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.243398113, -1.643398113}
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