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Simplifying -1v2 = 6v + -2 Reorder the terms: -1v2 = -2 + 6v Solving -1v2 = -2 + 6v Solving for variable 'v'. Reorder the terms: 2 + -6v + -1v2 = -2 + 6v + 2 + -6v Reorder the terms: 2 + -6v + -1v2 = -2 + 2 + 6v + -6v Combine like terms: -2 + 2 = 0 2 + -6v + -1v2 = 0 + 6v + -6v 2 + -6v + -1v2 = 6v + -6v Combine like terms: 6v + -6v = 0 2 + -6v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 6v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 6v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6v + v2 = 0 + 2 6v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 6v + v2 = 2 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 = 2 + 9 Reorder the terms: 9 + 6v + v2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6v + v2 = 11 Factor a perfect square on the left side: (v + 3)(v + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (v + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
v + 3 = 3.31662479 Simplifying v + 3 = 3.31662479 Reorder the terms: 3 + v = 3.31662479 Solving 3 + v = 3.31662479 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 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + v = 3.31662479 + -3 v = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 v = 0.31662479 Simplifying v = 0.31662479Subproblem 2
v + 3 = -3.31662479 Simplifying v + 3 = -3.31662479 Reorder the terms: 3 + v = -3.31662479 Solving 3 + v = -3.31662479 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 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + v = -3.31662479 + -3 v = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 v = -6.31662479 Simplifying v = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.31662479, -6.31662479}
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