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Simplifying 42q2 + 17qw + -15w2 = 0 Reorder the terms: 17qw + 42q2 + -15w2 = 0 Solving 17qw + 42q2 + -15w2 = 0 Solving for variable 'q'. Factor a trinomial. (7q + -3w)(6q + 5w) = 0Subproblem 1
Set the factor '(7q + -3w)' equal to zero and attempt to solve: Simplifying 7q + -3w = 0 Solving 7q + -3w = 0 Move all terms containing q to the left, all other terms to the right. Add '3w' to each side of the equation. 7q + -3w + 3w = 0 + 3w Combine like terms: -3w + 3w = 0 7q + 0 = 0 + 3w 7q = 0 + 3w Remove the zero: 7q = 3w Divide each side by '7'. q = 0.4285714286w Simplifying q = 0.4285714286wSubproblem 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 = {0.4285714286w, -0.8333333333w}
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