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Simplifying v2 + -3v = 27 + 3v Reorder the terms: -3v + v2 = 27 + 3v Solving -3v + v2 = 27 + 3v Solving for variable 'v'. Reorder the terms: -27 + -3v + -3v + v2 = 27 + 3v + -27 + -3v Combine like terms: -3v + -3v = -6v -27 + -6v + v2 = 27 + 3v + -27 + -3v Reorder the terms: -27 + -6v + v2 = 27 + -27 + 3v + -3v Combine like terms: 27 + -27 = 0 -27 + -6v + v2 = 0 + 3v + -3v -27 + -6v + v2 = 3v + -3v Combine like terms: 3v + -3v = 0 -27 + -6v + v2 = 0 Factor a trinomial. (-3 + -1v)(9 + -1v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 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 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 2
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 = 9Solution
v = {-3, 9}
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