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Simplifying 8r2 + -12rs + 6rs + -9s2 = 0 Reorder the terms: -12rs + 6rs + 8r2 + -9s2 = 0 Combine like terms: -12rs + 6rs = -6rs -6rs + 8r2 + -9s2 = 0 Solving -6rs + 8r2 + -9s2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + -3s)(4r + 3s) = 0Subproblem 1
Set the factor '(2r + -3s)' equal to zero and attempt to solve: Simplifying 2r + -3s = 0 Solving 2r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. 2r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 2r + 0 = 0 + 3s 2r = 0 + 3s Remove the zero: 2r = 3s Divide each side by '2'. r = 1.5s Simplifying r = 1.5sSubproblem 2
Set the factor '(4r + 3s)' equal to zero and attempt to solve: Simplifying 4r + 3s = 0 Solving 4r + 3s = 0 Move all terms containing r to the left, all other terms to the right. Add '-3s' to each side of the equation. 4r + 3s + -3s = 0 + -3s Combine like terms: 3s + -3s = 0 4r + 0 = 0 + -3s 4r = 0 + -3s Remove the zero: 4r = -3s Divide each side by '4'. r = -0.75s Simplifying r = -0.75sSolution
r = {1.5s, -0.75s}
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