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Simplifying 4v2 = 10 + 18v Solving 4v2 = 10 + 18v Solving for variable 'v'. Reorder the terms: -10 + -18v + 4v2 = 10 + 18v + -10 + -18v Reorder the terms: -10 + -18v + 4v2 = 10 + -10 + 18v + -18v Combine like terms: 10 + -10 = 0 -10 + -18v + 4v2 = 0 + 18v + -18v -10 + -18v + 4v2 = 18v + -18v Combine like terms: 18v + -18v = 0 -10 + -18v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9v + 2v2) = 0 Factor a trinomial. 2((-1 + -2v)(5 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2v)' equal to zero and attempt to solve: Simplifying -1 + -2v = 0 Solving -1 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2v = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2v = 0 + 1 -2v = 0 + 1 Combine like terms: 0 + 1 = 1 -2v = 1 Divide each side by '-2'. v = -0.5 Simplifying v = -0.5Subproblem 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 = {-0.5, 5}
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