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Simplifying (3v + 1)(3v + 1) = 0 Reorder the terms: (1 + 3v)(3v + 1) = 0 Reorder the terms: (1 + 3v)(1 + 3v) = 0 Multiply (1 + 3v) * (1 + 3v) (1(1 + 3v) + 3v * (1 + 3v)) = 0 ((1 * 1 + 3v * 1) + 3v * (1 + 3v)) = 0 ((1 + 3v) + 3v * (1 + 3v)) = 0 (1 + 3v + (1 * 3v + 3v * 3v)) = 0 (1 + 3v + (3v + 9v2)) = 0 Combine like terms: 3v + 3v = 6v (1 + 6v + 9v2) = 0 Solving 1 + 6v + 9v2 = 0 Solving for variable 'v'. Factor a trinomial. (1 + 3v)(1 + 3v) = 0Subproblem 1
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 = -0.3333333333Subproblem 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 = {-0.3333333333, -0.3333333333}
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