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Simplifying 11v2 + 99 = 20v + 10v2 Reorder the terms: 99 + 11v2 = 20v + 10v2 Solving 99 + 11v2 = 20v + 10v2 Solving for variable 'v'. Reorder the terms: 99 + -20v + 11v2 + -10v2 = 20v + 10v2 + -20v + -10v2 Combine like terms: 11v2 + -10v2 = 1v2 99 + -20v + 1v2 = 20v + 10v2 + -20v + -10v2 Reorder the terms: 99 + -20v + 1v2 = 20v + -20v + 10v2 + -10v2 Combine like terms: 20v + -20v = 0 99 + -20v + 1v2 = 0 + 10v2 + -10v2 99 + -20v + 1v2 = 10v2 + -10v2 Combine like terms: 10v2 + -10v2 = 0 99 + -20v + 1v2 = 0 Factor a trinomial. (9 + -1v)(11 + -1v) = 0Subproblem 1
Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9Subproblem 2
Set the factor '(11 + -1v)' equal to zero and attempt to solve: Simplifying 11 + -1v = 0 Solving 11 + -1v = 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 + -1v = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1v = 0 + -11 -1v = 0 + -11 Combine like terms: 0 + -11 = -11 -1v = -11 Divide each side by '-1'. v = 11 Simplifying v = 11Solution
v = {9, 11}
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