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Simplifying 0 = 4v2 + 19v + 21 Reorder the terms: 0 = 21 + 19v + 4v2 Solving 0 = 21 + 19v + 4v2 Solving for variable 'v'. Combine like terms: 0 + -21 = -21 -21 + -19v + -4v2 = 21 + 19v + 4v2 + -21 + -19v + -4v2 Reorder the terms: -21 + -19v + -4v2 = 21 + -21 + 19v + -19v + 4v2 + -4v2 Combine like terms: 21 + -21 = 0 -21 + -19v + -4v2 = 0 + 19v + -19v + 4v2 + -4v2 -21 + -19v + -4v2 = 19v + -19v + 4v2 + -4v2 Combine like terms: 19v + -19v = 0 -21 + -19v + -4v2 = 0 + 4v2 + -4v2 -21 + -19v + -4v2 = 4v2 + -4v2 Combine like terms: 4v2 + -4v2 = 0 -21 + -19v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 19v + 4v2) = 0 Factor a trinomial. -1((3 + v)(7 + 4v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 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 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Subproblem 2
Set the factor '(7 + 4v)' equal to zero and attempt to solve: Simplifying 7 + 4v = 0 Solving 7 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4v = 0 + -7 4v = 0 + -7 Combine like terms: 0 + -7 = -7 4v = -7 Divide each side by '4'. v = -1.75 Simplifying v = -1.75Solution
v = {-3, -1.75}
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