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Simplifying 2v2 + -6v + 44 = (v + -6)(v + -6) Reorder the terms: 44 + -6v + 2v2 = (v + -6)(v + -6) Reorder the terms: 44 + -6v + 2v2 = (-6 + v)(v + -6) Reorder the terms: 44 + -6v + 2v2 = (-6 + v)(-6 + v) Multiply (-6 + v) * (-6 + v) 44 + -6v + 2v2 = (-6(-6 + v) + v(-6 + v)) 44 + -6v + 2v2 = ((-6 * -6 + v * -6) + v(-6 + v)) 44 + -6v + 2v2 = ((36 + -6v) + v(-6 + v)) 44 + -6v + 2v2 = (36 + -6v + (-6 * v + v * v)) 44 + -6v + 2v2 = (36 + -6v + (-6v + v2)) Combine like terms: -6v + -6v = -12v 44 + -6v + 2v2 = (36 + -12v + v2) Solving 44 + -6v + 2v2 = 36 + -12v + v2 Solving for variable 'v'. Reorder the terms: 44 + -36 + -6v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2 Combine like terms: 44 + -36 = 8 8 + -6v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2 Combine like terms: -6v + 12v = 6v 8 + 6v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 8 + 6v + 1v2 = 36 + -12v + v2 + -36 + 12v + -1v2 Reorder the terms: 8 + 6v + 1v2 = 36 + -36 + -12v + 12v + v2 + -1v2 Combine like terms: 36 + -36 = 0 8 + 6v + 1v2 = 0 + -12v + 12v + v2 + -1v2 8 + 6v + 1v2 = -12v + 12v + v2 + -1v2 Combine like terms: -12v + 12v = 0 8 + 6v + 1v2 = 0 + v2 + -1v2 8 + 6v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 8 + 6v + 1v2 = 0 Factor a trinomial. (4 + v)(2 + v) = 0Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 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 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Solution
v = {-4, -2}
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