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Simplifying 4v2 = 19v + 5 Reorder the terms: 4v2 = 5 + 19v Solving 4v2 = 5 + 19v Solving for variable 'v'. Reorder the terms: -5 + -19v + 4v2 = 5 + 19v + -5 + -19v Reorder the terms: -5 + -19v + 4v2 = 5 + -5 + 19v + -19v Combine like terms: 5 + -5 = 0 -5 + -19v + 4v2 = 0 + 19v + -19v -5 + -19v + 4v2 = 19v + -19v Combine like terms: 19v + -19v = 0 -5 + -19v + 4v2 = 0 Factor a trinomial. (-1 + -4v)(5 + -1v) = 0Subproblem 1
Set the factor '(-1 + -4v)' equal to zero and attempt to solve: Simplifying -1 + -4v = 0 Solving -1 + -4v = 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 + -4v = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4v = 0 + 1 -4v = 0 + 1 Combine like terms: 0 + 1 = 1 -4v = 1 Divide each side by '-4'. v = -0.25 Simplifying v = -0.25Subproblem 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 = {-0.25, 5}
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