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Simplifying 2v2 + 11v + -5 = v2 + 25 Reorder the terms: -5 + 11v + 2v2 = v2 + 25 Reorder the terms: -5 + 11v + 2v2 = 25 + v2 Solving -5 + 11v + 2v2 = 25 + v2 Solving for variable 'v'. Reorder the terms: -5 + -25 + 11v + 2v2 + -1v2 = 25 + v2 + -25 + -1v2 Combine like terms: -5 + -25 = -30 -30 + 11v + 2v2 + -1v2 = 25 + v2 + -25 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -30 + 11v + 1v2 = 25 + v2 + -25 + -1v2 Reorder the terms: -30 + 11v + 1v2 = 25 + -25 + v2 + -1v2 Combine like terms: 25 + -25 = 0 -30 + 11v + 1v2 = 0 + v2 + -1v2 -30 + 11v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -30 + 11v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 11v + 30 + v2 = 0 + 30 Reorder the terms: -30 + 30 + 11v + v2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11v + v2 = 0 + 30 11v + v2 = 0 + 30 Combine like terms: 0 + 30 = 30 11v + v2 = 30 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 = 30 + 30.25 Reorder the terms: 30.25 + 11v + v2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + 11v + v2 = 60.25 Factor a perfect square on the left side: (v + 5.5)(v + 5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (v + 5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
v + 5.5 = 7.762087348 Simplifying v + 5.5 = 7.762087348 Reorder the terms: 5.5 + v = 7.762087348 Solving 5.5 + v = 7.762087348 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 = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = 7.762087348 + -5.5 v = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 v = 2.262087348 Simplifying v = 2.262087348Subproblem 2
v + 5.5 = -7.762087348 Simplifying v + 5.5 = -7.762087348 Reorder the terms: 5.5 + v = -7.762087348 Solving 5.5 + v = -7.762087348 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 = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = -7.762087348 + -5.5 v = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 v = -13.262087348 Simplifying v = -13.262087348Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.262087348, -13.262087348}
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