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Simplifying 18v2 + -27vw + 10w2 = 0 Reorder the terms: -27vw + 18v2 + 10w2 = 0 Solving -27vw + 18v2 + 10w2 = 0 Solving for variable 'v'. Factor a trinomial. (6v + -5w)(3v + -2w) = 0Subproblem 1
Set the factor '(6v + -5w)' equal to zero and attempt to solve: Simplifying 6v + -5w = 0 Solving 6v + -5w = 0 Move all terms containing v to the left, all other terms to the right. Add '5w' to each side of the equation. 6v + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 6v + 0 = 0 + 5w 6v = 0 + 5w Remove the zero: 6v = 5w Divide each side by '6'. v = 0.8333333333w Simplifying v = 0.8333333333wSubproblem 2
Set the factor '(3v + -2w)' equal to zero and attempt to solve: Simplifying 3v + -2w = 0 Solving 3v + -2w = 0 Move all terms containing v to the left, all other terms to the right. Add '2w' to each side of the equation. 3v + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 3v + 0 = 0 + 2w 3v = 0 + 2w Remove the zero: 3v = 2w Divide each side by '3'. v = 0.6666666667w Simplifying v = 0.6666666667wSolution
v = {0.8333333333w, 0.6666666667w}
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