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Simplifying 10r2 + -8rs + 15rs + -12s2 = 0 Reorder the terms: -8rs + 15rs + 10r2 + -12s2 = 0 Combine like terms: -8rs + 15rs = 7rs 7rs + 10r2 + -12s2 = 0 Solving 7rs + 10r2 + -12s2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + -4s)(2r + 3s) = 0Subproblem 1
Set the factor '(5r + -4s)' equal to zero and attempt to solve: Simplifying 5r + -4s = 0 Solving 5r + -4s = 0 Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 5r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 5r + 0 = 0 + 4s 5r = 0 + 4s Remove the zero: 5r = 4s Divide each side by '5'. r = 0.8s Simplifying r = 0.8sSubproblem 2
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 = -1.5sSolution
r = {0.8s, -1.5s}
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