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Simplifying -12r2 + 15rs + 8rs + -10s2 = 0 Reorder the terms: 15rs + 8rs + -12r2 + -10s2 = 0 Combine like terms: 15rs + 8rs = 23rs 23rs + -12r2 + -10s2 = 0 Solving 23rs + -12r2 + -10s2 = 0 Solving for variable 'r'. Factor a trinomial. (-3r + 2s)(4r + -5s) = 0Subproblem 1
Set the factor '(-3r + 2s)' equal to zero and attempt to solve: Simplifying -3r + 2s = 0 Solving -3r + 2s = 0 Move all terms containing r to the left, all other terms to the right. Add '-2s' to each side of the equation. -3r + 2s + -2s = 0 + -2s Combine like terms: 2s + -2s = 0 -3r + 0 = 0 + -2s -3r = 0 + -2s Remove the zero: -3r = -2s Divide each side by '-3'. r = 0.6666666667s Simplifying r = 0.6666666667sSubproblem 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 = {0.6666666667s, 1.25s}
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