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Simplifying 20v2 = 48 + 44v Solving 20v2 = 48 + 44v Solving for variable 'v'. Reorder the terms: -48 + -44v + 20v2 = 48 + 44v + -48 + -44v Reorder the terms: -48 + -44v + 20v2 = 48 + -48 + 44v + -44v Combine like terms: 48 + -48 = 0 -48 + -44v + 20v2 = 0 + 44v + -44v -48 + -44v + 20v2 = 44v + -44v Combine like terms: 44v + -44v = 0 -48 + -44v + 20v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -11v + 5v2) = 0 Factor a trinomial. 4((-4 + -5v)(3 + -1v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -5v)' equal to zero and attempt to solve: Simplifying -4 + -5v = 0 Solving -4 + -5v = 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 + -5v = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5v = 0 + 4 -5v = 0 + 4 Combine like terms: 0 + 4 = 4 -5v = 4 Divide each side by '-5'. v = -0.8 Simplifying v = -0.8Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.8, 3}
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