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Simplifying 20q2 + -23qw + 6w2 = 0 Reorder the terms: -23qw + 20q2 + 6w2 = 0 Solving -23qw + 20q2 + 6w2 = 0 Solving for variable 'q'. Factor a trinomial. (4q + -3w)(5q + -2w) = 0Subproblem 1
Set the factor '(4q + -3w)' equal to zero and attempt to solve: Simplifying 4q + -3w = 0 Solving 4q + -3w = 0 Move all terms containing q to the left, all other terms to the right. Add '3w' to each side of the equation. 4q + -3w + 3w = 0 + 3w Combine like terms: -3w + 3w = 0 4q + 0 = 0 + 3w 4q = 0 + 3w Remove the zero: 4q = 3w Divide each side by '4'. q = 0.75w Simplifying q = 0.75wSubproblem 2
Set the factor '(5q + -2w)' equal to zero and attempt to solve: Simplifying 5q + -2w = 0 Solving 5q + -2w = 0 Move all terms containing q to the left, all other terms to the right. Add '2w' to each side of the equation. 5q + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 5q + 0 = 0 + 2w 5q = 0 + 2w Remove the zero: 5q = 2w Divide each side by '5'. q = 0.4w Simplifying q = 0.4wSolution
q = {0.75w, 0.4w}
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