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Simplifying 11v2 + 82v + 100 = -4v2 + -3v Reorder the terms: 100 + 82v + 11v2 = -4v2 + -3v Reorder the terms: 100 + 82v + 11v2 = -3v + -4v2 Solving 100 + 82v + 11v2 = -3v + -4v2 Solving for variable 'v'. Reorder the terms: 100 + 82v + 3v + 11v2 + 4v2 = -3v + -4v2 + 3v + 4v2 Combine like terms: 82v + 3v = 85v 100 + 85v + 11v2 + 4v2 = -3v + -4v2 + 3v + 4v2 Combine like terms: 11v2 + 4v2 = 15v2 100 + 85v + 15v2 = -3v + -4v2 + 3v + 4v2 Reorder the terms: 100 + 85v + 15v2 = -3v + 3v + -4v2 + 4v2 Combine like terms: -3v + 3v = 0 100 + 85v + 15v2 = 0 + -4v2 + 4v2 100 + 85v + 15v2 = -4v2 + 4v2 Combine like terms: -4v2 + 4v2 = 0 100 + 85v + 15v2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 17v + 3v2) = 0 Factor a trinomial. 5((4 + v)(5 + 3v)) = 0 Ignore the factor 5.Subproblem 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 '(5 + 3v)' equal to zero and attempt to solve: Simplifying 5 + 3v = 0 Solving 5 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3v = 0 + -5 3v = 0 + -5 Combine like terms: 0 + -5 = -5 3v = -5 Divide each side by '3'. v = -1.666666667 Simplifying v = -1.666666667Solution
v = {-4, -1.666666667}
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