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Simplifying v2 + 2v + -14 = -12 Reorder the terms: -14 + 2v + v2 = -12 Solving -14 + 2v + v2 = -12 Solving for variable 'v'. Reorder the terms: -14 + 12 + 2v + v2 = -12 + 12 Combine like terms: -14 + 12 = -2 -2 + 2v + v2 = -12 + 12 Combine like terms: -12 + 12 = 0 -2 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 2v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 2v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2v + v2 = 0 + 2 2v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 2v + v2 = 2 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 = 2 + 1 Reorder the terms: 1 + 2v + v2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2v + v2 = 3 Factor a perfect square on the left side: (v + 1)(v + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (v + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
v + 1 = 1.732050808 Simplifying v + 1 = 1.732050808 Reorder the terms: 1 + v = 1.732050808 Solving 1 + v = 1.732050808 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 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + v = 1.732050808 + -1 v = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 v = 0.732050808 Simplifying v = 0.732050808Subproblem 2
v + 1 = -1.732050808 Simplifying v + 1 = -1.732050808 Reorder the terms: 1 + v = -1.732050808 Solving 1 + v = -1.732050808 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 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + v = -1.732050808 + -1 v = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 v = -2.732050808 Simplifying v = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.732050808, -2.732050808}
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