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Simplifying -4v2 + v = 20 + -5v2 Reorder the terms: v + -4v2 = 20 + -5v2 Solving v + -4v2 = 20 + -5v2 Solving for variable 'v'. Reorder the terms: -20 + v + -4v2 + 5v2 = 20 + -5v2 + -20 + 5v2 Combine like terms: -4v2 + 5v2 = 1v2 -20 + v + 1v2 = 20 + -5v2 + -20 + 5v2 Reorder the terms: -20 + v + 1v2 = 20 + -20 + -5v2 + 5v2 Combine like terms: 20 + -20 = 0 -20 + v + 1v2 = 0 + -5v2 + 5v2 -20 + v + 1v2 = -5v2 + 5v2 Combine like terms: -5v2 + 5v2 = 0 -20 + v + 1v2 = 0 Factor a trinomial. (-5 + -1v)(4 + -1v) = 0Subproblem 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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