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Simplifying (4v + -1)(7 + -1v) = 0 Reorder the terms: (-1 + 4v)(7 + -1v) = 0 Multiply (-1 + 4v) * (7 + -1v) (-1(7 + -1v) + 4v * (7 + -1v)) = 0 ((7 * -1 + -1v * -1) + 4v * (7 + -1v)) = 0 ((-7 + 1v) + 4v * (7 + -1v)) = 0 (-7 + 1v + (7 * 4v + -1v * 4v)) = 0 (-7 + 1v + (28v + -4v2)) = 0 Combine like terms: 1v + 28v = 29v (-7 + 29v + -4v2) = 0 Solving -7 + 29v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + v)(1 + -4v) = 0Subproblem 1
Set the factor '(-7 + v)' equal to zero and attempt to solve: Simplifying -7 + v = 0 Solving -7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + v = 0 + 7 v = 0 + 7 Combine like terms: 0 + 7 = 7 v = 7 Simplifying v = 7Subproblem 2
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 = 0.25Solution
v = {7, 0.25}
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