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Simplifying 9v2 + -20 = 12v Reorder the terms: -20 + 9v2 = 12v Solving -20 + 9v2 = 12v Solving for variable 'v'. Reorder the terms: -20 + -12v + 9v2 = 12v + -12v Combine like terms: 12v + -12v = 0 -20 + -12v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -1.333333333v + v2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -1.333333333v + 2.222222222 + v2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -1.333333333v + v2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -1.333333333v + v2 = 0 + 2.222222222 -1.333333333v + v2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -1.333333333v + v2 = 2.222222222 The v term is -1.333333333v. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333v + 0.4444444442 + v2 = 2.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333v + v2 = 2.222222222 + 0.4444444442 Combine like terms: 2.222222222 + 0.4444444442 = 2.6666666662 0.4444444442 + -1.333333333v + v2 = 2.6666666662 Factor a perfect square on the left side: (v + -0.6666666665)(v + -0.6666666665) = 2.6666666662 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (v + -0.6666666665) equal to 1.632993162 and -1.632993162.Subproblem 1
v + -0.6666666665 = 1.632993162 Simplifying v + -0.6666666665 = 1.632993162 Reorder the terms: -0.6666666665 + v = 1.632993162 Solving -0.6666666665 + v = 1.632993162 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + v = 1.632993162 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + v = 1.632993162 + 0.6666666665 v = 1.632993162 + 0.6666666665 Combine like terms: 1.632993162 + 0.6666666665 = 2.2996598285 v = 2.2996598285 Simplifying v = 2.2996598285Subproblem 2
v + -0.6666666665 = -1.632993162 Simplifying v + -0.6666666665 = -1.632993162 Reorder the terms: -0.6666666665 + v = -1.632993162 Solving -0.6666666665 + v = -1.632993162 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + v = -1.632993162 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + v = -1.632993162 + 0.6666666665 v = -1.632993162 + 0.6666666665 Combine like terms: -1.632993162 + 0.6666666665 = -0.9663264955 v = -0.9663264955 Simplifying v = -0.9663264955Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.2996598285, -0.9663264955}
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