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Simplifying 45R2 + -120RS + 80S2 = 0 Reorder the terms: -120RS + 45R2 + 80S2 = 0 Solving -120RS + 45R2 + 80S2 = 0 Solving for variable 'R'. Factor out the Greatest Common Factor (GCF), '5'. 5(-24RS + 9R2 + 16S2) = 0 Factor a trinomial. 5((3R + -4S)(3R + -4S)) = 0 Ignore the factor 5.Subproblem 1
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 = 1.333333333SSubproblem 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 = {1.333333333S, 1.333333333S}
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