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Simplifying 20v2 + -84v + -84 = -4 Reorder the terms: -84 + -84v + 20v2 = -4 Solving -84 + -84v + 20v2 = -4 Solving for variable 'v'. Reorder the terms: -84 + 4 + -84v + 20v2 = -4 + 4 Combine like terms: -84 + 4 = -80 -80 + -84v + 20v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -80 + -84v + 20v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + -21v + 5v2) = 0 Factor a trinomial. 4((-4 + -5v)(5 + -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 '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 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 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Solution
v = {-0.8, 5}
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