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Simplifying v2 + -4v + 2 = 0 Reorder the terms: 2 + -4v + v2 = 0 Solving 2 + -4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4v + -2 + v2 = 0 + -2 Reorder the terms: 2 + -2 + -4v + v2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4v + v2 = 0 + -2 -4v + v2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4v + v2 = -2 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = -2 + 4 Reorder the terms: 4 + -4v + v2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4v + v2 = 2 Factor a perfect square on the left side: (v + -2)(v + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (v + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
v + -2 = 1.414213562 Simplifying v + -2 = 1.414213562 Reorder the terms: -2 + v = 1.414213562 Solving -2 + v = 1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + v = 1.414213562 + 2 v = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 v = 3.414213562 Simplifying v = 3.414213562Subproblem 2
v + -2 = -1.414213562 Simplifying v + -2 = -1.414213562 Reorder the terms: -2 + v = -1.414213562 Solving -2 + v = -1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + v = -1.414213562 + 2 v = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 v = 0.585786438 Simplifying v = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.414213562, 0.585786438}
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