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Simplifying 2v2 + -11v = v2 + -14 Reorder the terms: -11v + 2v2 = v2 + -14 Reorder the terms: -11v + 2v2 = -14 + v2 Solving -11v + 2v2 = -14 + v2 Solving for variable 'v'. Reorder the terms: 14 + -11v + 2v2 + -1v2 = -14 + v2 + 14 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 14 + -11v + 1v2 = -14 + v2 + 14 + -1v2 Reorder the terms: 14 + -11v + 1v2 = -14 + 14 + v2 + -1v2 Combine like terms: -14 + 14 = 0 14 + -11v + 1v2 = 0 + v2 + -1v2 14 + -11v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 14 + -11v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -11v + -14 + v2 = 0 + -14 Reorder the terms: 14 + -14 + -11v + v2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -11v + v2 = 0 + -14 -11v + v2 = 0 + -14 Combine like terms: 0 + -14 = -14 -11v + v2 = -14 The v term is -11v. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11v + 30.25 + v2 = -14 + 30.25 Reorder the terms: 30.25 + -11v + v2 = -14 + 30.25 Combine like terms: -14 + 30.25 = 16.25 30.25 + -11v + v2 = 16.25 Factor a perfect square on the left side: (v + -5.5)(v + -5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (v + -5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
v + -5.5 = 4.031128874 Simplifying v + -5.5 = 4.031128874 Reorder the terms: -5.5 + v = 4.031128874 Solving -5.5 + v = 4.031128874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = 4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 4.031128874 + 5.5 v = 4.031128874 + 5.5 Combine like terms: 4.031128874 + 5.5 = 9.531128874 v = 9.531128874 Simplifying v = 9.531128874Subproblem 2
v + -5.5 = -4.031128874 Simplifying v + -5.5 = -4.031128874 Reorder the terms: -5.5 + v = -4.031128874 Solving -5.5 + v = -4.031128874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = -4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -4.031128874 + 5.5 v = -4.031128874 + 5.5 Combine like terms: -4.031128874 + 5.5 = 1.468871126 v = 1.468871126 Simplifying v = 1.468871126Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.531128874, 1.468871126}
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