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Simplifying 2v2 + -10v + -20 = 8 Reorder the terms: -20 + -10v + 2v2 = 8 Solving -20 + -10v + 2v2 = 8 Solving for variable 'v'. Reorder the terms: -20 + -8 + -10v + 2v2 = 8 + -8 Combine like terms: -20 + -8 = -28 -28 + -10v + 2v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -28 + -10v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -5v + v2) = 0 Factor a trinomial. 2((-2 + -1v)(7 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 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 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 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 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {-2, 7}
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