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Simplifying 21v2 + 28v + 9 = 2 Reorder the terms: 9 + 28v + 21v2 = 2 Solving 9 + 28v + 21v2 = 2 Solving for variable 'v'. Reorder the terms: 9 + -2 + 28v + 21v2 = 2 + -2 Combine like terms: 9 + -2 = 7 7 + 28v + 21v2 = 2 + -2 Combine like terms: 2 + -2 = 0 7 + 28v + 21v2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 4v + 3v2) = 0 Factor a trinomial. 7((1 + v)(1 + 3v)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 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 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1Subproblem 2
Set the factor '(1 + 3v)' equal to zero and attempt to solve: Simplifying 1 + 3v = 0 Solving 1 + 3v = 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 + 3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3v = 0 + -1 3v = 0 + -1 Combine like terms: 0 + -1 = -1 3v = -1 Divide each side by '3'. v = -0.3333333333 Simplifying v = -0.3333333333Solution
v = {-1, -0.3333333333}
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