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Simplifying 2v2 + -13v + 15 + -1v2 + -6v + -9 = 0 Reorder the terms: 15 + -9 + -13v + -6v + 2v2 + -1v2 = 0 Combine like terms: 15 + -9 = 6 6 + -13v + -6v + 2v2 + -1v2 = 0 Combine like terms: -13v + -6v = -19v 6 + -19v + 2v2 + -1v2 = 0 Combine like terms: 2v2 + -1v2 = 1v2 6 + -19v + 1v2 = 0 Solving 6 + -19v + 1v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -19v + -6 + v2 = 0 + -6 Reorder the terms: 6 + -6 + -19v + v2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -19v + v2 = 0 + -6 -19v + v2 = 0 + -6 Combine like terms: 0 + -6 = -6 -19v + v2 = -6 The v term is -19v. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19v + 90.25 + v2 = -6 + 90.25 Reorder the terms: 90.25 + -19v + v2 = -6 + 90.25 Combine like terms: -6 + 90.25 = 84.25 90.25 + -19v + v2 = 84.25 Factor a perfect square on the left side: (v + -9.5)(v + -9.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (v + -9.5) equal to 9.178779875 and -9.178779875.Subproblem 1
v + -9.5 = 9.178779875 Simplifying v + -9.5 = 9.178779875 Reorder the terms: -9.5 + v = 9.178779875 Solving -9.5 + v = 9.178779875 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = 9.178779875 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = 9.178779875 + 9.5 v = 9.178779875 + 9.5 Combine like terms: 9.178779875 + 9.5 = 18.678779875 v = 18.678779875 Simplifying v = 18.678779875Subproblem 2
v + -9.5 = -9.178779875 Simplifying v + -9.5 = -9.178779875 Reorder the terms: -9.5 + v = -9.178779875 Solving -9.5 + v = -9.178779875 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = -9.178779875 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = -9.178779875 + 9.5 v = -9.178779875 + 9.5 Combine like terms: -9.178779875 + 9.5 = 0.321220125 v = 0.321220125 Simplifying v = 0.321220125Solution
The solution to the problem is based on the solutions from the subproblems. v = {18.678779875, 0.321220125}
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