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Simplifying 2v2 + -25v + 79 = v2 + -49 Reorder the terms: 79 + -25v + 2v2 = v2 + -49 Reorder the terms: 79 + -25v + 2v2 = -49 + v2 Solving 79 + -25v + 2v2 = -49 + v2 Solving for variable 'v'. Reorder the terms: 79 + 49 + -25v + 2v2 + -1v2 = -49 + v2 + 49 + -1v2 Combine like terms: 79 + 49 = 128 128 + -25v + 2v2 + -1v2 = -49 + v2 + 49 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 128 + -25v + 1v2 = -49 + v2 + 49 + -1v2 Reorder the terms: 128 + -25v + 1v2 = -49 + 49 + v2 + -1v2 Combine like terms: -49 + 49 = 0 128 + -25v + 1v2 = 0 + v2 + -1v2 128 + -25v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 128 + -25v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '-128' to each side of the equation. 128 + -25v + -128 + v2 = 0 + -128 Reorder the terms: 128 + -128 + -25v + v2 = 0 + -128 Combine like terms: 128 + -128 = 0 0 + -25v + v2 = 0 + -128 -25v + v2 = 0 + -128 Combine like terms: 0 + -128 = -128 -25v + v2 = -128 The v term is -25v. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25v + 156.25 + v2 = -128 + 156.25 Reorder the terms: 156.25 + -25v + v2 = -128 + 156.25 Combine like terms: -128 + 156.25 = 28.25 156.25 + -25v + v2 = 28.25 Factor a perfect square on the left side: (v + -12.5)(v + -12.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (v + -12.5) equal to 5.315072906 and -5.315072906.Subproblem 1
v + -12.5 = 5.315072906 Simplifying v + -12.5 = 5.315072906 Reorder the terms: -12.5 + v = 5.315072906 Solving -12.5 + v = 5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + v = 5.315072906 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + v = 5.315072906 + 12.5 v = 5.315072906 + 12.5 Combine like terms: 5.315072906 + 12.5 = 17.815072906 v = 17.815072906 Simplifying v = 17.815072906Subproblem 2
v + -12.5 = -5.315072906 Simplifying v + -12.5 = -5.315072906 Reorder the terms: -12.5 + v = -5.315072906 Solving -12.5 + v = -5.315072906 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + v = -5.315072906 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + v = -5.315072906 + 12.5 v = -5.315072906 + 12.5 Combine like terms: -5.315072906 + 12.5 = 7.184927094 v = 7.184927094 Simplifying v = 7.184927094Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.815072906, 7.184927094}
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