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Simplifying v2 + 2v = 14 Reorder the terms: 2v + v2 = 14 Solving 2v + v2 = 14 Solving for variable 'v'. Reorder the terms: -14 + 2v + v2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2v + 14 + v2 = 0 + 14 Reorder the terms: -14 + 14 + 2v + v2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2v + v2 = 0 + 14 2v + v2 = 0 + 14 Combine like terms: 0 + 14 = 14 2v + v2 = 14 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 = 14 + 1 Reorder the terms: 1 + 2v + v2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2v + v2 = 15 Factor a perfect square on the left side: (v + 1)(v + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (v + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
v + 1 = 3.872983346 Simplifying v + 1 = 3.872983346 Reorder the terms: 1 + v = 3.872983346 Solving 1 + v = 3.872983346 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 = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + v = 3.872983346 + -1 v = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 v = 2.872983346 Simplifying v = 2.872983346Subproblem 2
v + 1 = -3.872983346 Simplifying v + 1 = -3.872983346 Reorder the terms: 1 + v = -3.872983346 Solving 1 + v = -3.872983346 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 = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + v = -3.872983346 + -1 v = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 v = -4.872983346 Simplifying v = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.872983346, -4.872983346}
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