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Simplifying v2 + -6v + -34 = -4 Reorder the terms: -34 + -6v + v2 = -4 Solving -34 + -6v + v2 = -4 Solving for variable 'v'. Reorder the terms: -34 + 4 + -6v + v2 = -4 + 4 Combine like terms: -34 + 4 = -30 -30 + -6v + v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -30 + -6v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -6v + 30 + v2 = 0 + 30 Reorder the terms: -30 + 30 + -6v + v2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -6v + v2 = 0 + 30 -6v + v2 = 0 + 30 Combine like terms: 0 + 30 = 30 -6v + v2 = 30 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = 30 + 9 Reorder the terms: 9 + -6v + v2 = 30 + 9 Combine like terms: 30 + 9 = 39 9 + -6v + v2 = 39 Factor a perfect square on the left side: (v + -3)(v + -3) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (v + -3) equal to 6.244997998 and -6.244997998.Subproblem 1
v + -3 = 6.244997998 Simplifying v + -3 = 6.244997998 Reorder the terms: -3 + v = 6.244997998 Solving -3 + v = 6.244997998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + v = 6.244997998 + 3 v = 6.244997998 + 3 Combine like terms: 6.244997998 + 3 = 9.244997998 v = 9.244997998 Simplifying v = 9.244997998Subproblem 2
v + -3 = -6.244997998 Simplifying v + -3 = -6.244997998 Reorder the terms: -3 + v = -6.244997998 Solving -3 + v = -6.244997998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + v = -6.244997998 + 3 v = -6.244997998 + 3 Combine like terms: -6.244997998 + 3 = -3.244997998 v = -3.244997998 Simplifying v = -3.244997998Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.244997998, -3.244997998}
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