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Simplifying 4v2 + 11v + -116 = 3 Reorder the terms: -116 + 11v + 4v2 = 3 Solving -116 + 11v + 4v2 = 3 Solving for variable 'v'. Reorder the terms: -116 + -3 + 11v + 4v2 = 3 + -3 Combine like terms: -116 + -3 = -119 -119 + 11v + 4v2 = 3 + -3 Combine like terms: 3 + -3 = 0 -119 + 11v + 4v2 = 0 Factor a trinomial. (-7 + -1v)(17 + -4v) = 0Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 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 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7Subproblem 2
Set the factor '(17 + -4v)' equal to zero and attempt to solve: Simplifying 17 + -4v = 0 Solving 17 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -4v = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -4v = 0 + -17 -4v = 0 + -17 Combine like terms: 0 + -17 = -17 -4v = -17 Divide each side by '-4'. v = 4.25 Simplifying v = 4.25Solution
v = {-7, 4.25}
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