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Simplifying 2v2 = 90 + 8v Solving 2v2 = 90 + 8v Solving for variable 'v'. Reorder the terms: -90 + -8v + 2v2 = 90 + 8v + -90 + -8v Reorder the terms: -90 + -8v + 2v2 = 90 + -90 + 8v + -8v Combine like terms: 90 + -90 = 0 -90 + -8v + 2v2 = 0 + 8v + -8v -90 + -8v + 2v2 = 8v + -8v Combine like terms: 8v + -8v = 0 -90 + -8v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -4v + v2) = 0 Factor a trinomial. 2((-5 + -1v)(9 + -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 '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9Solution
v = {-5, 9}
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