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Simplifying v2 + 14v + 41 = 8 Reorder the terms: 41 + 14v + v2 = 8 Solving 41 + 14v + v2 = 8 Solving for variable 'v'. Reorder the terms: 41 + -8 + 14v + v2 = 8 + -8 Combine like terms: 41 + -8 = 33 33 + 14v + v2 = 8 + -8 Combine like terms: 8 + -8 = 0 33 + 14v + v2 = 0 Factor a trinomial. (11 + v)(3 + v) = 0Subproblem 1
Set the factor '(11 + v)' equal to zero and attempt to solve: Simplifying 11 + v = 0 Solving 11 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + v = 0 + -11 Combine like terms: 11 + -11 = 0 0 + v = 0 + -11 v = 0 + -11 Combine like terms: 0 + -11 = -11 v = -11 Simplifying v = -11Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Solution
v = {-11, -3}
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