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Simplifying 6r2 + -5rs + s2 = 0 Reorder the terms: -5rs + 6r2 + s2 = 0 Solving -5rs + 6r2 + s2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + -1s)(3r + -1s) = 0Subproblem 1
Set the factor '(2r + -1s)' equal to zero and attempt to solve: Simplifying 2r + -1s = 0 Solving 2r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 2r + -1s + s = 0 + s Combine like terms: -1s + s = 0 2r + 0 = 0 + s 2r = 0 + s Remove the zero: 2r = s Divide each side by '2'. r = 0.5s Simplifying r = 0.5sSubproblem 2
Set the factor '(3r + -1s)' equal to zero and attempt to solve: Simplifying 3r + -1s = 0 Solving 3r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 3r + -1s + s = 0 + s Combine like terms: -1s + s = 0 3r + 0 = 0 + s 3r = 0 + s Remove the zero: 3r = s Divide each side by '3'. r = 0.3333333333s Simplifying r = 0.3333333333sSolution
r = {0.5s, 0.3333333333s}
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