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Simplifying v2 + -11v + -2 = 0 Reorder the terms: -2 + -11v + v2 = 0 Solving -2 + -11v + 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 + -11v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + -11v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -11v + v2 = 0 + 2 -11v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 -11v + v2 = 2 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 = 2 + 30.25 Reorder the terms: 30.25 + -11v + v2 = 2 + 30.25 Combine like terms: 2 + 30.25 = 32.25 30.25 + -11v + v2 = 32.25 Factor a perfect square on the left side: (v + -5.5)(v + -5.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (v + -5.5) equal to 5.678908346 and -5.678908346.Subproblem 1
v + -5.5 = 5.678908346 Simplifying v + -5.5 = 5.678908346 Reorder the terms: -5.5 + v = 5.678908346 Solving -5.5 + v = 5.678908346 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 = 5.678908346 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 5.678908346 + 5.5 v = 5.678908346 + 5.5 Combine like terms: 5.678908346 + 5.5 = 11.178908346 v = 11.178908346 Simplifying v = 11.178908346Subproblem 2
v + -5.5 = -5.678908346 Simplifying v + -5.5 = -5.678908346 Reorder the terms: -5.5 + v = -5.678908346 Solving -5.5 + v = -5.678908346 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 = -5.678908346 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -5.678908346 + 5.5 v = -5.678908346 + 5.5 Combine like terms: -5.678908346 + 5.5 = -0.178908346 v = -0.178908346 Simplifying v = -0.178908346Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.178908346, -0.178908346}
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