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Simplifying v2 + 6v + -1 = 0 Reorder the terms: -1 + 6v + v2 = 0 Solving -1 + 6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 6v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6v + v2 = 0 + 1 6v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 6v + v2 = 1 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 = 1 + 9 Reorder the terms: 9 + 6v + v2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6v + v2 = 10 Factor a perfect square on the left side: (v + 3)(v + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (v + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
v + 3 = 3.16227766 Simplifying v + 3 = 3.16227766 Reorder the terms: 3 + v = 3.16227766 Solving 3 + v = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + v = 3.16227766 + -3 v = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 v = 0.16227766 Simplifying v = 0.16227766Subproblem 2
v + 3 = -3.16227766 Simplifying v + 3 = -3.16227766 Reorder the terms: 3 + v = -3.16227766 Solving 3 + v = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + v = -3.16227766 + -3 v = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 v = -6.16227766 Simplifying v = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.16227766, -6.16227766}
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