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Simplifying (3v2 + -6v + -4) + (5v2 + -1v + 2) = 0 Reorder the terms: (-4 + -6v + 3v2) + (5v2 + -1v + 2) = 0 Remove parenthesis around (-4 + -6v + 3v2) -4 + -6v + 3v2 + (5v2 + -1v + 2) = 0 Reorder the terms: -4 + -6v + 3v2 + (2 + -1v + 5v2) = 0 Remove parenthesis around (2 + -1v + 5v2) -4 + -6v + 3v2 + 2 + -1v + 5v2 = 0 Reorder the terms: -4 + 2 + -6v + -1v + 3v2 + 5v2 = 0 Combine like terms: -4 + 2 = -2 -2 + -6v + -1v + 3v2 + 5v2 = 0 Combine like terms: -6v + -1v = -7v -2 + -7v + 3v2 + 5v2 = 0 Combine like terms: 3v2 + 5v2 = 8v2 -2 + -7v + 8v2 = 0 Solving -2 + -7v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -0.875v + v2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.875v + 0.25 + v2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.875v + v2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.875v + v2 = 0 + 0.25 -0.875v + v2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.875v + v2 = 0.25 The v term is -0.875v. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875v + 0.19140625 + v2 = 0.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875v + v2 = 0.25 + 0.19140625 Combine like terms: 0.25 + 0.19140625 = 0.44140625 0.19140625 + -0.875v + v2 = 0.44140625 Factor a perfect square on the left side: (v + -0.4375)(v + -0.4375) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (v + -0.4375) equal to 0.664384113 and -0.664384113.Subproblem 1
v + -0.4375 = 0.664384113 Simplifying v + -0.4375 = 0.664384113 Reorder the terms: -0.4375 + v = 0.664384113 Solving -0.4375 + v = 0.664384113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + v = 0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + v = 0.664384113 + 0.4375 v = 0.664384113 + 0.4375 Combine like terms: 0.664384113 + 0.4375 = 1.101884113 v = 1.101884113 Simplifying v = 1.101884113Subproblem 2
v + -0.4375 = -0.664384113 Simplifying v + -0.4375 = -0.664384113 Reorder the terms: -0.4375 + v = -0.664384113 Solving -0.4375 + v = -0.664384113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + v = -0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + v = -0.664384113 + 0.4375 v = -0.664384113 + 0.4375 Combine like terms: -0.664384113 + 0.4375 = -0.226884113 v = -0.226884113 Simplifying v = -0.226884113Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.101884113, -0.226884113}
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