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Simplifying (8 + v)(4v + 1) = 0 Reorder the terms: (8 + v)(1 + 4v) = 0 Multiply (8 + v) * (1 + 4v) (8(1 + 4v) + v(1 + 4v)) = 0 ((1 * 8 + 4v * 8) + v(1 + 4v)) = 0 ((8 + 32v) + v(1 + 4v)) = 0 (8 + 32v + (1 * v + 4v * v)) = 0 (8 + 32v + (1v + 4v2)) = 0 Combine like terms: 32v + 1v = 33v (8 + 33v + 4v2) = 0 Solving 8 + 33v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + v)(1 + 4v) = 0Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve: Simplifying 8 + v = 0 Solving 8 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + v = 0 + -8 v = 0 + -8 Combine like terms: 0 + -8 = -8 v = -8 Simplifying v = -8Subproblem 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 = {-8, -0.25}
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