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Simplifying (4v2 + -7v + -3) + (6v2 + -2v + 1) = 0 Reorder the terms: (-3 + -7v + 4v2) + (6v2 + -2v + 1) = 0 Remove parenthesis around (-3 + -7v + 4v2) -3 + -7v + 4v2 + (6v2 + -2v + 1) = 0 Reorder the terms: -3 + -7v + 4v2 + (1 + -2v + 6v2) = 0 Remove parenthesis around (1 + -2v + 6v2) -3 + -7v + 4v2 + 1 + -2v + 6v2 = 0 Reorder the terms: -3 + 1 + -7v + -2v + 4v2 + 6v2 = 0 Combine like terms: -3 + 1 = -2 -2 + -7v + -2v + 4v2 + 6v2 = 0 Combine like terms: -7v + -2v = -9v -2 + -9v + 4v2 + 6v2 = 0 Combine like terms: 4v2 + 6v2 = 10v2 -2 + -9v + 10v2 = 0 Solving -2 + -9v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -0.9v + v2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.9v + 0.2 + v2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.9v + v2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.9v + v2 = 0.0 + 0.2 -0.9v + v2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -0.9v + v2 = 0.2 The v term is -0.9v. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9v + 0.2025 + v2 = 0.2 + 0.2025 Reorder the terms: 0.2025 + -0.9v + v2 = 0.2 + 0.2025 Combine like terms: 0.2 + 0.2025 = 0.4025 0.2025 + -0.9v + v2 = 0.4025 Factor a perfect square on the left side: (v + -0.45)(v + -0.45) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (v + -0.45) equal to 0.634428877 and -0.634428877.Subproblem 1
v + -0.45 = 0.634428877 Simplifying v + -0.45 = 0.634428877 Reorder the terms: -0.45 + v = 0.634428877 Solving -0.45 + v = 0.634428877 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + v = 0.634428877 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + v = 0.634428877 + 0.45 v = 0.634428877 + 0.45 Combine like terms: 0.634428877 + 0.45 = 1.084428877 v = 1.084428877 Simplifying v = 1.084428877Subproblem 2
v + -0.45 = -0.634428877 Simplifying v + -0.45 = -0.634428877 Reorder the terms: -0.45 + v = -0.634428877 Solving -0.45 + v = -0.634428877 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + v = -0.634428877 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + v = -0.634428877 + 0.45 v = -0.634428877 + 0.45 Combine like terms: -0.634428877 + 0.45 = -0.184428877 v = -0.184428877 Simplifying v = -0.184428877Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.084428877, -0.184428877}
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