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Simplifying 4v2 + -53v + 125 = 0 Reorder the terms: 125 + -53v + 4v2 = 0 Solving 125 + -53v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 31.25 + -13.25v + v2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + -13.25v + -31.25 + v2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + -13.25v + v2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + -13.25v + v2 = 0 + -31.25 -13.25v + v2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 -13.25v + v2 = -31.25 The v term is -13.25v. Take half its coefficient (-6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. -13.25v + 43.890625 + v2 = -31.25 + 43.890625 Reorder the terms: 43.890625 + -13.25v + v2 = -31.25 + 43.890625 Combine like terms: -31.25 + 43.890625 = 12.640625 43.890625 + -13.25v + v2 = 12.640625 Factor a perfect square on the left side: (v + -6.625)(v + -6.625) = 12.640625 Calculate the square root of the right side: 3.555365663 Break this problem into two subproblems by setting (v + -6.625) equal to 3.555365663 and -3.555365663.Subproblem 1
v + -6.625 = 3.555365663 Simplifying v + -6.625 = 3.555365663 Reorder the terms: -6.625 + v = 3.555365663 Solving -6.625 + v = 3.555365663 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + v = 3.555365663 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + v = 3.555365663 + 6.625 v = 3.555365663 + 6.625 Combine like terms: 3.555365663 + 6.625 = 10.180365663 v = 10.180365663 Simplifying v = 10.180365663Subproblem 2
v + -6.625 = -3.555365663 Simplifying v + -6.625 = -3.555365663 Reorder the terms: -6.625 + v = -3.555365663 Solving -6.625 + v = -3.555365663 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + v = -3.555365663 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + v = -3.555365663 + 6.625 v = -3.555365663 + 6.625 Combine like terms: -3.555365663 + 6.625 = 3.069634337 v = 3.069634337 Simplifying v = 3.069634337Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.180365663, 3.069634337}
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