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Simplifying -1v2 + 46v + 32 = 8 + -8v2 Reorder the terms: 32 + 46v + -1v2 = 8 + -8v2 Solving 32 + 46v + -1v2 = 8 + -8v2 Solving for variable 'v'. Reorder the terms: 32 + -8 + 46v + -1v2 + 8v2 = 8 + -8v2 + -8 + 8v2 Combine like terms: 32 + -8 = 24 24 + 46v + -1v2 + 8v2 = 8 + -8v2 + -8 + 8v2 Combine like terms: -1v2 + 8v2 = 7v2 24 + 46v + 7v2 = 8 + -8v2 + -8 + 8v2 Reorder the terms: 24 + 46v + 7v2 = 8 + -8 + -8v2 + 8v2 Combine like terms: 8 + -8 = 0 24 + 46v + 7v2 = 0 + -8v2 + 8v2 24 + 46v + 7v2 = -8v2 + 8v2 Combine like terms: -8v2 + 8v2 = 0 24 + 46v + 7v2 = 0 Factor a trinomial. (6 + v)(4 + 7v) = 0Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6Subproblem 2
Set the factor '(4 + 7v)' equal to zero and attempt to solve: Simplifying 4 + 7v = 0 Solving 4 + 7v = 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 + 7v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7v = 0 + -4 7v = 0 + -4 Combine like terms: 0 + -4 = -4 7v = -4 Divide each side by '7'. v = -0.5714285714 Simplifying v = -0.5714285714Solution
v = {-6, -0.5714285714}
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