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Simplifying v2 + -14v + 14 = -6 Reorder the terms: 14 + -14v + v2 = -6 Solving 14 + -14v + v2 = -6 Solving for variable 'v'. Reorder the terms: 14 + 6 + -14v + v2 = -6 + 6 Combine like terms: 14 + 6 = 20 20 + -14v + v2 = -6 + 6 Combine like terms: -6 + 6 = 0 20 + -14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -14v + -20 + v2 = 0 + -20 Reorder the terms: 20 + -20 + -14v + v2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -14v + v2 = 0 + -20 -14v + v2 = 0 + -20 Combine like terms: 0 + -20 = -20 -14v + v2 = -20 The v term is -14v. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14v + 49 + v2 = -20 + 49 Reorder the terms: 49 + -14v + v2 = -20 + 49 Combine like terms: -20 + 49 = 29 49 + -14v + v2 = 29 Factor a perfect square on the left side: (v + -7)(v + -7) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (v + -7) equal to 5.385164807 and -5.385164807.Subproblem 1
v + -7 = 5.385164807 Simplifying v + -7 = 5.385164807 Reorder the terms: -7 + v = 5.385164807 Solving -7 + v = 5.385164807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = 5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + v = 5.385164807 + 7 v = 5.385164807 + 7 Combine like terms: 5.385164807 + 7 = 12.385164807 v = 12.385164807 Simplifying v = 12.385164807Subproblem 2
v + -7 = -5.385164807 Simplifying v + -7 = -5.385164807 Reorder the terms: -7 + v = -5.385164807 Solving -7 + v = -5.385164807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = -5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + v = -5.385164807 + 7 v = -5.385164807 + 7 Combine like terms: -5.385164807 + 7 = 1.614835193 v = 1.614835193 Simplifying v = 1.614835193Solution
The solution to the problem is based on the solutions from the subproblems. v = {12.385164807, 1.614835193}
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