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Simplifying (2v2 + -1v + 5) + (-6v2 + 3v + 4) = 0 Reorder the terms: (5 + -1v + 2v2) + (-6v2 + 3v + 4) = 0 Remove parenthesis around (5 + -1v + 2v2) 5 + -1v + 2v2 + (-6v2 + 3v + 4) = 0 Reorder the terms: 5 + -1v + 2v2 + (4 + 3v + -6v2) = 0 Remove parenthesis around (4 + 3v + -6v2) 5 + -1v + 2v2 + 4 + 3v + -6v2 = 0 Reorder the terms: 5 + 4 + -1v + 3v + 2v2 + -6v2 = 0 Combine like terms: 5 + 4 = 9 9 + -1v + 3v + 2v2 + -6v2 = 0 Combine like terms: -1v + 3v = 2v 9 + 2v + 2v2 + -6v2 = 0 Combine like terms: 2v2 + -6v2 = -4v2 9 + 2v + -4v2 = 0 Solving 9 + 2v + -4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -0.5v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.5v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.5v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.5v + v2 = 0 + 2.25 -0.5v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.5v + v2 = 2.25 The v term is -0.5v. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5v + 0.0625 + v2 = 2.25 + 0.0625 Reorder the terms: 0.0625 + -0.5v + v2 = 2.25 + 0.0625 Combine like terms: 2.25 + 0.0625 = 2.3125 0.0625 + -0.5v + v2 = 2.3125 Factor a perfect square on the left side: (v + -0.25)(v + -0.25) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (v + -0.25) equal to 1.520690633 and -1.520690633.Subproblem 1
v + -0.25 = 1.520690633 Simplifying v + -0.25 = 1.520690633 Reorder the terms: -0.25 + v = 1.520690633 Solving -0.25 + v = 1.520690633 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + v = 1.520690633 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = 1.520690633 + 0.25 v = 1.520690633 + 0.25 Combine like terms: 1.520690633 + 0.25 = 1.770690633 v = 1.770690633 Simplifying v = 1.770690633Subproblem 2
v + -0.25 = -1.520690633 Simplifying v + -0.25 = -1.520690633 Reorder the terms: -0.25 + v = -1.520690633 Solving -0.25 + v = -1.520690633 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + v = -1.520690633 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = -1.520690633 + 0.25 v = -1.520690633 + 0.25 Combine like terms: -1.520690633 + 0.25 = -1.270690633 v = -1.270690633 Simplifying v = -1.270690633Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.770690633, -1.270690633}
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