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Simplifying 12r2 + 13rs + -4s2 = 0 Reorder the terms: 13rs + 12r2 + -4s2 = 0 Solving 13rs + 12r2 + -4s2 = 0 Solving for variable 'r'. Factor a trinomial. (4r + -1s)(3r + 4s) = 0Subproblem 1
Set the factor '(4r + -1s)' equal to zero and attempt to solve: Simplifying 4r + -1s = 0 Solving 4r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 4r + -1s + s = 0 + s Combine like terms: -1s + s = 0 4r + 0 = 0 + s 4r = 0 + s Remove the zero: 4r = s Divide each side by '4'. r = 0.25s Simplifying r = 0.25sSubproblem 2
Set the factor '(3r + 4s)' equal to zero and attempt to solve: Simplifying 3r + 4s = 0 Solving 3r + 4s = 0 Move all terms containing r to the left, all other terms to the right. Add '-4s' to each side of the equation. 3r + 4s + -4s = 0 + -4s Combine like terms: 4s + -4s = 0 3r + 0 = 0 + -4s 3r = 0 + -4s Remove the zero: 3r = -4s Divide each side by '3'. r = -1.333333333s Simplifying r = -1.333333333sSolution
r = {0.25s, -1.333333333s}
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