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Simplifying 12r2 + -20rs + 15rs + -25s2 = 0 Reorder the terms: -20rs + 15rs + 12r2 + -25s2 = 0 Combine like terms: -20rs + 15rs = -5rs -5rs + 12r2 + -25s2 = 0 Solving -5rs + 12r2 + -25s2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + -5s)(4r + 5s) = 0Subproblem 1
Set the factor '(3r + -5s)' equal to zero and attempt to solve: Simplifying 3r + -5s = 0 Solving 3r + -5s = 0 Move all terms containing r to the left, all other terms to the right. Add '5s' to each side of the equation. 3r + -5s + 5s = 0 + 5s Combine like terms: -5s + 5s = 0 3r + 0 = 0 + 5s 3r = 0 + 5s Remove the zero: 3r = 5s Divide each side by '3'. r = 1.666666667s Simplifying r = 1.666666667sSubproblem 2
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 = -1.25sSolution
r = {1.666666667s, -1.25s}
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