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Simplifying 2v2 + -18v + 32 + -1v + -25 = 0 Reorder the terms: 32 + -25 + -18v + -1v + 2v2 = 0 Combine like terms: 32 + -25 = 7 7 + -18v + -1v + 2v2 = 0 Combine like terms: -18v + -1v = -19v 7 + -19v + 2v2 = 0 Solving 7 + -19v + 2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -9.5v + v2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -9.5v + -3.5 + v2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -9.5v + v2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -9.5v + v2 = 0 + -3.5 -9.5v + v2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -9.5v + v2 = -3.5 The v term is -9.5v. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5v + 22.5625 + v2 = -3.5 + 22.5625 Reorder the terms: 22.5625 + -9.5v + v2 = -3.5 + 22.5625 Combine like terms: -3.5 + 22.5625 = 19.0625 22.5625 + -9.5v + v2 = 19.0625 Factor a perfect square on the left side: (v + -4.75)(v + -4.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (v + -4.75) equal to 4.366062299 and -4.366062299.Subproblem 1
v + -4.75 = 4.366062299 Simplifying v + -4.75 = 4.366062299 Reorder the terms: -4.75 + v = 4.366062299 Solving -4.75 + v = 4.366062299 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + v = 4.366062299 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + v = 4.366062299 + 4.75 v = 4.366062299 + 4.75 Combine like terms: 4.366062299 + 4.75 = 9.116062299 v = 9.116062299 Simplifying v = 9.116062299Subproblem 2
v + -4.75 = -4.366062299 Simplifying v + -4.75 = -4.366062299 Reorder the terms: -4.75 + v = -4.366062299 Solving -4.75 + v = -4.366062299 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + v = -4.366062299 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + v = -4.366062299 + 4.75 v = -4.366062299 + 4.75 Combine like terms: -4.366062299 + 4.75 = 0.383937701 v = 0.383937701 Simplifying v = 0.383937701Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.116062299, 0.383937701}
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