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Simplifying 9v2 + -19 = 7v2 + 11v Reorder the terms: -19 + 9v2 = 7v2 + 11v Reorder the terms: -19 + 9v2 = 11v + 7v2 Solving -19 + 9v2 = 11v + 7v2 Solving for variable 'v'. Reorder the terms: -19 + -11v + 9v2 + -7v2 = 11v + 7v2 + -11v + -7v2 Combine like terms: 9v2 + -7v2 = 2v2 -19 + -11v + 2v2 = 11v + 7v2 + -11v + -7v2 Reorder the terms: -19 + -11v + 2v2 = 11v + -11v + 7v2 + -7v2 Combine like terms: 11v + -11v = 0 -19 + -11v + 2v2 = 0 + 7v2 + -7v2 -19 + -11v + 2v2 = 7v2 + -7v2 Combine like terms: 7v2 + -7v2 = 0 -19 + -11v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -5.5v + v2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -5.5v + 9.5 + v2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -5.5v + v2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -5.5v + v2 = 0 + 9.5 -5.5v + v2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -5.5v + v2 = 9.5 The v term is -5.5v. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5v + 7.5625 + v2 = 9.5 + 7.5625 Reorder the terms: 7.5625 + -5.5v + v2 = 9.5 + 7.5625 Combine like terms: 9.5 + 7.5625 = 17.0625 7.5625 + -5.5v + v2 = 17.0625 Factor a perfect square on the left side: (v + -2.75)(v + -2.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (v + -2.75) equal to 4.13067791 and -4.13067791.Subproblem 1
v + -2.75 = 4.13067791 Simplifying v + -2.75 = 4.13067791 Reorder the terms: -2.75 + v = 4.13067791 Solving -2.75 + v = 4.13067791 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + v = 4.13067791 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + v = 4.13067791 + 2.75 v = 4.13067791 + 2.75 Combine like terms: 4.13067791 + 2.75 = 6.88067791 v = 6.88067791 Simplifying v = 6.88067791Subproblem 2
v + -2.75 = -4.13067791 Simplifying v + -2.75 = -4.13067791 Reorder the terms: -2.75 + v = -4.13067791 Solving -2.75 + v = -4.13067791 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + v = -4.13067791 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + v = -4.13067791 + 2.75 v = -4.13067791 + 2.75 Combine like terms: -4.13067791 + 2.75 = -1.38067791 v = -1.38067791 Simplifying v = -1.38067791Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.88067791, -1.38067791}
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