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Simplifying (4v2 + 3v + -9) + (-2v2 + -6v + -3) + -1(-7v2 + -2v + 7) = 0 Reorder the terms: (-9 + 3v + 4v2) + (-2v2 + -6v + -3) + -1(-7v2 + -2v + 7) = 0 Remove parenthesis around (-9 + 3v + 4v2) -9 + 3v + 4v2 + (-2v2 + -6v + -3) + -1(-7v2 + -2v + 7) = 0 Reorder the terms: -9 + 3v + 4v2 + (-3 + -6v + -2v2) + -1(-7v2 + -2v + 7) = 0 Remove parenthesis around (-3 + -6v + -2v2) -9 + 3v + 4v2 + -3 + -6v + -2v2 + -1(-7v2 + -2v + 7) = 0 Reorder the terms: -9 + 3v + 4v2 + -3 + -6v + -2v2 + -1(7 + -2v + -7v2) = 0 -9 + 3v + 4v2 + -3 + -6v + -2v2 + (7 * -1 + -2v * -1 + -7v2 * -1) = 0 -9 + 3v + 4v2 + -3 + -6v + -2v2 + (-7 + 2v + 7v2) = 0 Reorder the terms: -9 + -3 + -7 + 3v + -6v + 2v + 4v2 + -2v2 + 7v2 = 0 Combine like terms: -9 + -3 = -12 -12 + -7 + 3v + -6v + 2v + 4v2 + -2v2 + 7v2 = 0 Combine like terms: -12 + -7 = -19 -19 + 3v + -6v + 2v + 4v2 + -2v2 + 7v2 = 0 Combine like terms: 3v + -6v = -3v -19 + -3v + 2v + 4v2 + -2v2 + 7v2 = 0 Combine like terms: -3v + 2v = -1v -19 + -1v + 4v2 + -2v2 + 7v2 = 0 Combine like terms: 4v2 + -2v2 = 2v2 -19 + -1v + 2v2 + 7v2 = 0 Combine like terms: 2v2 + 7v2 = 9v2 -19 + -1v + 9v2 = 0 Solving -19 + -1v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.111111111 + -0.1111111111v + v2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + -0.1111111111v + 2.111111111 + v2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + -0.1111111111v + v2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + -0.1111111111v + v2 = 0 + 2.111111111 -0.1111111111v + v2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 -0.1111111111v + v2 = 2.111111111 The v term is -0.1111111111v. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111v + 0.003086419752 + v2 = 2.111111111 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111v + v2 = 2.111111111 + 0.003086419752 Combine like terms: 2.111111111 + 0.003086419752 = 2.114197530752 0.003086419752 + -0.1111111111v + v2 = 2.114197530752 Factor a perfect square on the left side: (v + -0.05555555555)(v + -0.05555555555) = 2.114197530752 Calculate the square root of the right side: 1.454028036 Break this problem into two subproblems by setting (v + -0.05555555555) equal to 1.454028036 and -1.454028036.Subproblem 1
v + -0.05555555555 = 1.454028036 Simplifying v + -0.05555555555 = 1.454028036 Reorder the terms: -0.05555555555 + v = 1.454028036 Solving -0.05555555555 + v = 1.454028036 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + v = 1.454028036 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + v = 1.454028036 + 0.05555555555 v = 1.454028036 + 0.05555555555 Combine like terms: 1.454028036 + 0.05555555555 = 1.50958359155 v = 1.50958359155 Simplifying v = 1.50958359155Subproblem 2
v + -0.05555555555 = -1.454028036 Simplifying v + -0.05555555555 = -1.454028036 Reorder the terms: -0.05555555555 + v = -1.454028036 Solving -0.05555555555 + v = -1.454028036 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + v = -1.454028036 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + v = -1.454028036 + 0.05555555555 v = -1.454028036 + 0.05555555555 Combine like terms: -1.454028036 + 0.05555555555 = -1.39847248045 v = -1.39847248045 Simplifying v = -1.39847248045Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.50958359155, -1.39847248045}
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