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Simplifying 60q2 + -34qw + -70w2 = 0 Reorder the terms: -34qw + 60q2 + -70w2 = 0 Solving -34qw + 60q2 + -70w2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17qw + 30q2 + -35w2) = 0 Factor a trinomial. 2((5q + -7w)(6q + 5w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5q + -7w)' equal to zero and attempt to solve: Simplifying 5q + -7w = 0 Solving 5q + -7w = 0 Move all terms containing q to the left, all other terms to the right. Add '7w' to each side of the equation. 5q + -7w + 7w = 0 + 7w Combine like terms: -7w + 7w = 0 5q + 0 = 0 + 7w 5q = 0 + 7w Remove the zero: 5q = 7w Divide each side by '5'. q = 1.4w Simplifying q = 1.4wSubproblem 2
Set the factor '(6q + 5w)' equal to zero and attempt to solve: Simplifying 6q + 5w = 0 Solving 6q + 5w = 0 Move all terms containing q to the left, all other terms to the right. Add '-5w' to each side of the equation. 6q + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 6q + 0 = 0 + -5w 6q = 0 + -5w Remove the zero: 6q = -5w Divide each side by '6'. q = -0.8333333333w Simplifying q = -0.8333333333wSolution
q = {1.4w, -0.8333333333w}
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