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Simplifying (3v2 + -4v + -4) + (5v2 + -6v + -6) + -1(3v2 + 5v + -3) = 0 Reorder the terms: (-4 + -4v + 3v2) + (5v2 + -6v + -6) + -1(3v2 + 5v + -3) = 0 Remove parenthesis around (-4 + -4v + 3v2) -4 + -4v + 3v2 + (5v2 + -6v + -6) + -1(3v2 + 5v + -3) = 0 Reorder the terms: -4 + -4v + 3v2 + (-6 + -6v + 5v2) + -1(3v2 + 5v + -3) = 0 Remove parenthesis around (-6 + -6v + 5v2) -4 + -4v + 3v2 + -6 + -6v + 5v2 + -1(3v2 + 5v + -3) = 0 Reorder the terms: -4 + -4v + 3v2 + -6 + -6v + 5v2 + -1(-3 + 5v + 3v2) = 0 -4 + -4v + 3v2 + -6 + -6v + 5v2 + (-3 * -1 + 5v * -1 + 3v2 * -1) = 0 -4 + -4v + 3v2 + -6 + -6v + 5v2 + (3 + -5v + -3v2) = 0 Reorder the terms: -4 + -6 + 3 + -4v + -6v + -5v + 3v2 + 5v2 + -3v2 = 0 Combine like terms: -4 + -6 = -10 -10 + 3 + -4v + -6v + -5v + 3v2 + 5v2 + -3v2 = 0 Combine like terms: -10 + 3 = -7 -7 + -4v + -6v + -5v + 3v2 + 5v2 + -3v2 = 0 Combine like terms: -4v + -6v = -10v -7 + -10v + -5v + 3v2 + 5v2 + -3v2 = 0 Combine like terms: -10v + -5v = -15v -7 + -15v + 3v2 + 5v2 + -3v2 = 0 Combine like terms: 3v2 + 5v2 = 8v2 -7 + -15v + 8v2 + -3v2 = 0 Combine like terms: 8v2 + -3v2 = 5v2 -7 + -15v + 5v2 = 0 Solving -7 + -15v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -3v + v2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -3v + 1.4 + v2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -3v + v2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -3v + v2 = 0 + 1.4 -3v + v2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -3v + v2 = 1.4 The v term is -3v. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3v + 2.25 + v2 = 1.4 + 2.25 Reorder the terms: 2.25 + -3v + v2 = 1.4 + 2.25 Combine like terms: 1.4 + 2.25 = 3.65 2.25 + -3v + v2 = 3.65 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 3.65 Calculate the square root of the right side: 1.910497317 Break this problem into two subproblems by setting (v + -1.5) equal to 1.910497317 and -1.910497317.Subproblem 1
v + -1.5 = 1.910497317 Simplifying v + -1.5 = 1.910497317 Reorder the terms: -1.5 + v = 1.910497317 Solving -1.5 + v = 1.910497317 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = 1.910497317 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 1.910497317 + 1.5 v = 1.910497317 + 1.5 Combine like terms: 1.910497317 + 1.5 = 3.410497317 v = 3.410497317 Simplifying v = 3.410497317Subproblem 2
v + -1.5 = -1.910497317 Simplifying v + -1.5 = -1.910497317 Reorder the terms: -1.5 + v = -1.910497317 Solving -1.5 + v = -1.910497317 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = -1.910497317 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -1.910497317 + 1.5 v = -1.910497317 + 1.5 Combine like terms: -1.910497317 + 1.5 = -0.410497317 v = -0.410497317 Simplifying v = -0.410497317Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.410497317, -0.410497317}
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