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Simplifying 15r2 + -4rs + -3s2 = 0 Reorder the terms: -4rs + 15r2 + -3s2 = 0 Solving -4rs + 15r2 + -3s2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + -3s)(3r + s) = 0Subproblem 1
Set the factor '(5r + -3s)' equal to zero and attempt to solve: Simplifying 5r + -3s = 0 Solving 5r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. 5r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 5r + 0 = 0 + 3s 5r = 0 + 3s Remove the zero: 5r = 3s Divide each side by '5'. r = 0.6s Simplifying r = 0.6sSubproblem 2
Set the factor '(3r + s)' equal to zero and attempt to solve: Simplifying 3r + s = 0 Solving 3r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 3r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 3r + 0 = 0 + -1s 3r = 0 + -1s Remove the zero: 3r = -1s Divide each side by '3'. r = -0.3333333333s Simplifying r = -0.3333333333sSolution
r = {0.6s, -0.3333333333s}
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