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Simplifying v2 + 2v = 27 Reorder the terms: 2v + v2 = 27 Solving 2v + v2 = 27 Solving for variable 'v'. Reorder the terms: -27 + 2v + v2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 2v + 27 + v2 = 0 + 27 Reorder the terms: -27 + 27 + 2v + v2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 2v + v2 = 0 + 27 2v + v2 = 0 + 27 Combine like terms: 0 + 27 = 27 2v + v2 = 27 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 27 + 1 Reorder the terms: 1 + 2v + v2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + 2v + v2 = 28 Factor a perfect square on the left side: (v + 1)(v + 1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (v + 1) equal to 5.291502622 and -5.291502622.Subproblem 1
v + 1 = 5.291502622 Simplifying v + 1 = 5.291502622 Reorder the terms: 1 + v = 5.291502622 Solving 1 + v = 5.291502622 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + v = 5.291502622 + -1 v = 5.291502622 + -1 Combine like terms: 5.291502622 + -1 = 4.291502622 v = 4.291502622 Simplifying v = 4.291502622Subproblem 2
v + 1 = -5.291502622 Simplifying v + 1 = -5.291502622 Reorder the terms: 1 + v = -5.291502622 Solving 1 + v = -5.291502622 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + v = -5.291502622 + -1 v = -5.291502622 + -1 Combine like terms: -5.291502622 + -1 = -6.291502622 v = -6.291502622 Simplifying v = -6.291502622Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.291502622, -6.291502622}
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