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Simplifying 20q2 + 13qw + -15w2 = 0 Reorder the terms: 13qw + 20q2 + -15w2 = 0 Solving 13qw + 20q2 + -15w2 = 0 Solving for variable 'q'. Factor a trinomial. (5q + -3w)(4q + 5w) = 0Subproblem 1
Set the factor '(5q + -3w)' equal to zero and attempt to solve: Simplifying 5q + -3w = 0 Solving 5q + -3w = 0 Move all terms containing q to the left, all other terms to the right. Add '3w' to each side of the equation. 5q + -3w + 3w = 0 + 3w Combine like terms: -3w + 3w = 0 5q + 0 = 0 + 3w 5q = 0 + 3w Remove the zero: 5q = 3w Divide each side by '5'. q = 0.6w Simplifying q = 0.6wSubproblem 2
Set the factor '(4q + 5w)' equal to zero and attempt to solve: Simplifying 4q + 5w = 0 Solving 4q + 5w = 0 Move all terms containing q to the left, all other terms to the right. Add '-5w' to each side of the equation. 4q + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 4q + 0 = 0 + -5w 4q = 0 + -5w Remove the zero: 4q = -5w Divide each side by '4'. q = -1.25w Simplifying q = -1.25wSolution
q = {0.6w, -1.25w}
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