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Simplifying 12r2 + 13rs + -35s2 = 0 Reorder the terms: 13rs + 12r2 + -35s2 = 0 Solving 13rs + 12r2 + -35s2 = 0 Solving for variable 'r'. Factor a trinomial. (4r + -5s)(3r + 7s) = 0Subproblem 1
Set the factor '(4r + -5s)' equal to zero and attempt to solve: Simplifying 4r + -5s = 0 Solving 4r + -5s = 0 Move all terms containing r to the left, all other terms to the right. Add '5s' to each side of the equation. 4r + -5s + 5s = 0 + 5s Combine like terms: -5s + 5s = 0 4r + 0 = 0 + 5s 4r = 0 + 5s Remove the zero: 4r = 5s Divide each side by '4'. r = 1.25s Simplifying r = 1.25sSubproblem 2
Set the factor '(3r + 7s)' equal to zero and attempt to solve: Simplifying 3r + 7s = 0 Solving 3r + 7s = 0 Move all terms containing r to the left, all other terms to the right. Add '-7s' to each side of the equation. 3r + 7s + -7s = 0 + -7s Combine like terms: 7s + -7s = 0 3r + 0 = 0 + -7s 3r = 0 + -7s Remove the zero: 3r = -7s Divide each side by '3'. r = -2.333333333s Simplifying r = -2.333333333sSolution
r = {1.25s, -2.333333333s}
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