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Simplifying (5v2 + -1v + -3) + (6v2 + -4v + 2) = 0 Reorder the terms: (-3 + -1v + 5v2) + (6v2 + -4v + 2) = 0 Remove parenthesis around (-3 + -1v + 5v2) -3 + -1v + 5v2 + (6v2 + -4v + 2) = 0 Reorder the terms: -3 + -1v + 5v2 + (2 + -4v + 6v2) = 0 Remove parenthesis around (2 + -4v + 6v2) -3 + -1v + 5v2 + 2 + -4v + 6v2 = 0 Reorder the terms: -3 + 2 + -1v + -4v + 5v2 + 6v2 = 0 Combine like terms: -3 + 2 = -1 -1 + -1v + -4v + 5v2 + 6v2 = 0 Combine like terms: -1v + -4v = -5v -1 + -5v + 5v2 + 6v2 = 0 Combine like terms: 5v2 + 6v2 = 11v2 -1 + -5v + 11v2 = 0 Solving -1 + -5v + 11v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -0.4545454545v + v2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.4545454545v + 0.09090909091 + v2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.4545454545v + v2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.4545454545v + v2 = 0 + 0.09090909091 -0.4545454545v + v2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.4545454545v + v2 = 0.09090909091 The v term is -0.4545454545v. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545v + 0.05165289257 + v2 = 0.09090909091 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545v + v2 = 0.09090909091 + 0.05165289257 Combine like terms: 0.09090909091 + 0.05165289257 = 0.14256198348 0.05165289257 + -0.4545454545v + v2 = 0.14256198348 Factor a perfect square on the left side: (v + -0.2272727273)(v + -0.2272727273) = 0.14256198348 Calculate the square root of the right side: 0.377573812 Break this problem into two subproblems by setting (v + -0.2272727273) equal to 0.377573812 and -0.377573812.Subproblem 1
v + -0.2272727273 = 0.377573812 Simplifying v + -0.2272727273 = 0.377573812 Reorder the terms: -0.2272727273 + v = 0.377573812 Solving -0.2272727273 + v = 0.377573812 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + v = 0.377573812 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + v = 0.377573812 + 0.2272727273 v = 0.377573812 + 0.2272727273 Combine like terms: 0.377573812 + 0.2272727273 = 0.6048465393 v = 0.6048465393 Simplifying v = 0.6048465393Subproblem 2
v + -0.2272727273 = -0.377573812 Simplifying v + -0.2272727273 = -0.377573812 Reorder the terms: -0.2272727273 + v = -0.377573812 Solving -0.2272727273 + v = -0.377573812 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + v = -0.377573812 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + v = -0.377573812 + 0.2272727273 v = -0.377573812 + 0.2272727273 Combine like terms: -0.377573812 + 0.2272727273 = -0.1503010847 v = -0.1503010847 Simplifying v = -0.1503010847Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.6048465393, -0.1503010847}
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