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Simplifying (7v2 + -5v + -4) + (6v2 + -3v + 2) = 0 Reorder the terms: (-4 + -5v + 7v2) + (6v2 + -3v + 2) = 0 Remove parenthesis around (-4 + -5v + 7v2) -4 + -5v + 7v2 + (6v2 + -3v + 2) = 0 Reorder the terms: -4 + -5v + 7v2 + (2 + -3v + 6v2) = 0 Remove parenthesis around (2 + -3v + 6v2) -4 + -5v + 7v2 + 2 + -3v + 6v2 = 0 Reorder the terms: -4 + 2 + -5v + -3v + 7v2 + 6v2 = 0 Combine like terms: -4 + 2 = -2 -2 + -5v + -3v + 7v2 + 6v2 = 0 Combine like terms: -5v + -3v = -8v -2 + -8v + 7v2 + 6v2 = 0 Combine like terms: 7v2 + 6v2 = 13v2 -2 + -8v + 13v2 = 0 Solving -2 + -8v + 13v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.1538461538 + -0.6153846154v + v2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -0.6153846154v + 0.1538461538 + v2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -0.6153846154v + v2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -0.6153846154v + v2 = 0 + 0.1538461538 -0.6153846154v + v2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -0.6153846154v + v2 = 0.1538461538 The v term is -0.6153846154v. Take half its coefficient (-0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. -0.6153846154v + 0.09467455622 + v2 = 0.1538461538 + 0.09467455622 Reorder the terms: 0.09467455622 + -0.6153846154v + v2 = 0.1538461538 + 0.09467455622 Combine like terms: 0.1538461538 + 0.09467455622 = 0.24852071002 0.09467455622 + -0.6153846154v + v2 = 0.24852071002 Factor a perfect square on the left side: (v + -0.3076923077)(v + -0.3076923077) = 0.24852071002 Calculate the square root of the right side: 0.498518515 Break this problem into two subproblems by setting (v + -0.3076923077) equal to 0.498518515 and -0.498518515.Subproblem 1
v + -0.3076923077 = 0.498518515 Simplifying v + -0.3076923077 = 0.498518515 Reorder the terms: -0.3076923077 + v = 0.498518515 Solving -0.3076923077 + v = 0.498518515 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + v = 0.498518515 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + v = 0.498518515 + 0.3076923077 v = 0.498518515 + 0.3076923077 Combine like terms: 0.498518515 + 0.3076923077 = 0.8062108227 v = 0.8062108227 Simplifying v = 0.8062108227Subproblem 2
v + -0.3076923077 = -0.498518515 Simplifying v + -0.3076923077 = -0.498518515 Reorder the terms: -0.3076923077 + v = -0.498518515 Solving -0.3076923077 + v = -0.498518515 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + v = -0.498518515 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + v = -0.498518515 + 0.3076923077 v = -0.498518515 + 0.3076923077 Combine like terms: -0.498518515 + 0.3076923077 = -0.1908262073 v = -0.1908262073 Simplifying v = -0.1908262073Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.8062108227, -0.1908262073}
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