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Simplifying v2 + -14v + 22 = 5 Reorder the terms: 22 + -14v + v2 = 5 Solving 22 + -14v + v2 = 5 Solving for variable 'v'. Reorder the terms: 22 + -5 + -14v + v2 = 5 + -5 Combine like terms: 22 + -5 = 17 17 + -14v + v2 = 5 + -5 Combine like terms: 5 + -5 = 0 17 + -14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -14v + -17 + v2 = 0 + -17 Reorder the terms: 17 + -17 + -14v + v2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -14v + v2 = 0 + -17 -14v + v2 = 0 + -17 Combine like terms: 0 + -17 = -17 -14v + v2 = -17 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 = -17 + 49 Reorder the terms: 49 + -14v + v2 = -17 + 49 Combine like terms: -17 + 49 = 32 49 + -14v + v2 = 32 Factor a perfect square on the left side: (v + -7)(v + -7) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (v + -7) equal to 5.656854249 and -5.656854249.Subproblem 1
v + -7 = 5.656854249 Simplifying v + -7 = 5.656854249 Reorder the terms: -7 + v = 5.656854249 Solving -7 + v = 5.656854249 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 = 5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + v = 5.656854249 + 7 v = 5.656854249 + 7 Combine like terms: 5.656854249 + 7 = 12.656854249 v = 12.656854249 Simplifying v = 12.656854249Subproblem 2
v + -7 = -5.656854249 Simplifying v + -7 = -5.656854249 Reorder the terms: -7 + v = -5.656854249 Solving -7 + v = -5.656854249 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 = -5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + v = -5.656854249 + 7 v = -5.656854249 + 7 Combine like terms: -5.656854249 + 7 = 1.343145751 v = 1.343145751 Simplifying v = 1.343145751Solution
The solution to the problem is based on the solutions from the subproblems. v = {12.656854249, 1.343145751}
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