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Simplifying v2 + 6v + 7 = 0 Reorder the terms: 7 + 6v + v2 = 0 Solving 7 + 6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6v + -7 + v2 = 0 + -7 Reorder the terms: 7 + -7 + 6v + v2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6v + v2 = 0 + -7 6v + v2 = 0 + -7 Combine like terms: 0 + -7 = -7 6v + v2 = -7 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 = -7 + 9 Reorder the terms: 9 + 6v + v2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6v + v2 = 2 Factor a perfect square on the left side: (v + 3)(v + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (v + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
v + 3 = 1.414213562 Simplifying v + 3 = 1.414213562 Reorder the terms: 3 + v = 1.414213562 Solving 3 + v = 1.414213562 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 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + v = 1.414213562 + -3 v = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 v = -1.585786438 Simplifying v = -1.585786438Subproblem 2
v + 3 = -1.414213562 Simplifying v + 3 = -1.414213562 Reorder the terms: 3 + v = -1.414213562 Solving 3 + v = -1.414213562 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 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + v = -1.414213562 + -3 v = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 v = -4.414213562 Simplifying v = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.585786438, -4.414213562}
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