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Simplifying v2 + -9v = 8 Reorder the terms: -9v + v2 = 8 Solving -9v + v2 = 8 Solving for variable 'v'. Reorder the terms: -8 + -9v + v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -9v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -9v + 8 + v2 = 0 + 8 Reorder the terms: -8 + 8 + -9v + v2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9v + v2 = 0 + 8 -9v + v2 = 0 + 8 Combine like terms: 0 + 8 = 8 -9v + v2 = 8 The v term is -9v. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9v + 20.25 + v2 = 8 + 20.25 Reorder the terms: 20.25 + -9v + v2 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + -9v + v2 = 28.25 Factor a perfect square on the left side: (v + -4.5)(v + -4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (v + -4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
v + -4.5 = 5.315072906 Simplifying v + -4.5 = 5.315072906 Reorder the terms: -4.5 + v = 5.315072906 Solving -4.5 + v = 5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = 5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 5.315072906 + 4.5 v = 5.315072906 + 4.5 Combine like terms: 5.315072906 + 4.5 = 9.815072906 v = 9.815072906 Simplifying v = 9.815072906Subproblem 2
v + -4.5 = -5.315072906 Simplifying v + -4.5 = -5.315072906 Reorder the terms: -4.5 + v = -5.315072906 Solving -4.5 + v = -5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = -5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -5.315072906 + 4.5 v = -5.315072906 + 4.5 Combine like terms: -5.315072906 + 4.5 = -0.815072906 v = -0.815072906 Simplifying v = -0.815072906Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.815072906, -0.815072906}
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