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Simplifying 20q2 + -9qr + -18r2 = 0 Reorder the terms: -9qr + 20q2 + -18r2 = 0 Solving -9qr + 20q2 + -18r2 = 0 Solving for variable 'q'. Factor a trinomial. (5q + -6r)(4q + 3r) = 0Subproblem 1
Set the factor '(5q + -6r)' equal to zero and attempt to solve: Simplifying 5q + -6r = 0 Solving 5q + -6r = 0 Move all terms containing q to the left, all other terms to the right. Add '6r' to each side of the equation. 5q + -6r + 6r = 0 + 6r Combine like terms: -6r + 6r = 0 5q + 0 = 0 + 6r 5q = 0 + 6r Remove the zero: 5q = 6r Divide each side by '5'. q = 1.2r Simplifying q = 1.2rSubproblem 2
Set the factor '(4q + 3r)' equal to zero and attempt to solve: Simplifying 4q + 3r = 0 Solving 4q + 3r = 0 Move all terms containing q to the left, all other terms to the right. Add '-3r' to each side of the equation. 4q + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 4q + 0 = 0 + -3r 4q = 0 + -3r Remove the zero: 4q = -3r Divide each side by '4'. q = -0.75r Simplifying q = -0.75rSolution
q = {1.2r, -0.75r}
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