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Simplifying 2v2 = 40 + -2v Solving 2v2 = 40 + -2v Solving for variable 'v'. Reorder the terms: -40 + 2v + 2v2 = 40 + -2v + -40 + 2v Reorder the terms: -40 + 2v + 2v2 = 40 + -40 + -2v + 2v Combine like terms: 40 + -40 = 0 -40 + 2v + 2v2 = 0 + -2v + 2v -40 + 2v + 2v2 = -2v + 2v Combine like terms: -2v + 2v = 0 -40 + 2v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + v + v2) = 0 Factor a trinomial. 2((-5 + -1v)(4 + -1v)) = 0 Ignore the factor 2.Subproblem 1
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 = -5Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 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 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Solution
v = {-5, 4}
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