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Simplifying 18q2 + -33qw + 14w2 = 0 Reorder the terms: -33qw + 18q2 + 14w2 = 0 Solving -33qw + 18q2 + 14w2 = 0 Solving for variable 'q'. Factor a trinomial. (6q + -7w)(3q + -2w) = 0Subproblem 1
Set the factor '(6q + -7w)' equal to zero and attempt to solve: Simplifying 6q + -7w = 0 Solving 6q + -7w = 0 Move all terms containing q to the left, all other terms to the right. Add '7w' to each side of the equation. 6q + -7w + 7w = 0 + 7w Combine like terms: -7w + 7w = 0 6q + 0 = 0 + 7w 6q = 0 + 7w Remove the zero: 6q = 7w Divide each side by '6'. q = 1.166666667w Simplifying q = 1.166666667wSubproblem 2
Set the factor '(3q + -2w)' equal to zero and attempt to solve: Simplifying 3q + -2w = 0 Solving 3q + -2w = 0 Move all terms containing q to the left, all other terms to the right. Add '2w' to each side of the equation. 3q + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 3q + 0 = 0 + 2w 3q = 0 + 2w Remove the zero: 3q = 2w Divide each side by '3'. q = 0.6666666667w Simplifying q = 0.6666666667wSolution
q = {1.166666667w, 0.6666666667w}
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