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Simplifying 25q2 + 5qr + -6r2 = 0 Reorder the terms: 5qr + 25q2 + -6r2 = 0 Solving 5qr + 25q2 + -6r2 = 0 Solving for variable 'q'. Factor a trinomial. (5q + -2r)(5q + 3r) = 0Subproblem 1
Set the factor '(5q + -2r)' equal to zero and attempt to solve: Simplifying 5q + -2r = 0 Solving 5q + -2r = 0 Move all terms containing q to the left, all other terms to the right. Add '2r' to each side of the equation. 5q + -2r + 2r = 0 + 2r Combine like terms: -2r + 2r = 0 5q + 0 = 0 + 2r 5q = 0 + 2r Remove the zero: 5q = 2r Divide each side by '5'. q = 0.4r Simplifying q = 0.4rSubproblem 2
Set the factor '(5q + 3r)' equal to zero and attempt to solve: Simplifying 5q + 3r = 0 Solving 5q + 3r = 0 Move all terms containing q to the left, all other terms to the right. Add '-3r' to each side of the equation. 5q + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 5q + 0 = 0 + -3r 5q = 0 + -3r Remove the zero: 5q = -3r Divide each side by '5'. q = -0.6r Simplifying q = -0.6rSolution
q = {0.4r, -0.6r}
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