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Simplifying v2 + -2v + -1 = 0 Reorder the terms: -1 + -2v + v2 = 0 Solving -1 + -2v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -2v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -2v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2v + v2 = 0 + 1 -2v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2v + v2 = 1 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 1 + 1 Reorder the terms: 1 + -2v + v2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2v + v2 = 2 Factor a perfect square on the left side: (v + -1)(v + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (v + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
v + -1 = 1.414213562 Simplifying v + -1 = 1.414213562 Reorder the terms: -1 + v = 1.414213562 Solving -1 + v = 1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + v = 1.414213562 + 1 v = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 v = 2.414213562 Simplifying v = 2.414213562Subproblem 2
v + -1 = -1.414213562 Simplifying v + -1 = -1.414213562 Reorder the terms: -1 + v = -1.414213562 Solving -1 + v = -1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + v = -1.414213562 + 1 v = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 v = -0.414213562 Simplifying v = -0.414213562Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.414213562, -0.414213562}
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