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