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Simplifying (2v2 + -5v + -3) + -1(4v2 + -9v + -8) + (7v2 + 3v + -3) = 0 Reorder the terms: (-3 + -5v + 2v2) + -1(4v2 + -9v + -8) + (7v2 + 3v + -3) = 0 Remove parenthesis around (-3 + -5v + 2v2) -3 + -5v + 2v2 + -1(4v2 + -9v + -8) + (7v2 + 3v + -3) = 0 Reorder the terms: -3 + -5v + 2v2 + -1(-8 + -9v + 4v2) + (7v2 + 3v + -3) = 0 -3 + -5v + 2v2 + (-8 * -1 + -9v * -1 + 4v2 * -1) + (7v2 + 3v + -3) = 0 -3 + -5v + 2v2 + (8 + 9v + -4v2) + (7v2 + 3v + -3) = 0 Reorder the terms: -3 + -5v + 2v2 + 8 + 9v + -4v2 + (-3 + 3v + 7v2) = 0 Remove parenthesis around (-3 + 3v + 7v2) -3 + -5v + 2v2 + 8 + 9v + -4v2 + -3 + 3v + 7v2 = 0 Reorder the terms: -3 + 8 + -3 + -5v + 9v + 3v + 2v2 + -4v2 + 7v2 = 0 Combine like terms: -3 + 8 = 5 5 + -3 + -5v + 9v + 3v + 2v2 + -4v2 + 7v2 = 0 Combine like terms: 5 + -3 = 2 2 + -5v + 9v + 3v + 2v2 + -4v2 + 7v2 = 0 Combine like terms: -5v + 9v = 4v 2 + 4v + 3v + 2v2 + -4v2 + 7v2 = 0 Combine like terms: 4v + 3v = 7v 2 + 7v + 2v2 + -4v2 + 7v2 = 0 Combine like terms: 2v2 + -4v2 = -2v2 2 + 7v + -2v2 + 7v2 = 0 Combine like terms: -2v2 + 7v2 = 5v2 2 + 7v + 5v2 = 0 Solving 2 + 7v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (1 + v)(2 + 5v) = 0Subproblem 1
Set the factor '(1 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1Subproblem 2
Set the factor '(2 + 5v)' equal to zero and attempt to solve: Simplifying 2 + 5v = 0 Solving 2 + 5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5v = 0 + -2 5v = 0 + -2 Combine like terms: 0 + -2 = -2 5v = -2 Divide each side by '5'. v = -0.4 Simplifying v = -0.4Solution
v = {-1, -0.4}
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