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Simplifying 54s2 + 120st + 66t2 = 0 Reorder the terms: 120st + 54s2 + 66t2 = 0 Solving 120st + 54s2 + 66t2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '6'. 6(20st + 9s2 + 11t2) = 0 Factor a trinomial. 6((s + t)(9s + 11t)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(s + t)' equal to zero and attempt to solve: Simplifying s + t = 0 Solving s + t = 0 Move all terms containing s to the left, all other terms to the right. Add '-1t' to each side of the equation. s + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 s + 0 = 0 + -1t s = 0 + -1t Remove the zero: s = -1t Simplifying s = -1tSubproblem 2
Set the factor '(9s + 11t)' equal to zero and attempt to solve: Simplifying 9s + 11t = 0 Solving 9s + 11t = 0 Move all terms containing s to the left, all other terms to the right. Add '-11t' to each side of the equation. 9s + 11t + -11t = 0 + -11t Combine like terms: 11t + -11t = 0 9s + 0 = 0 + -11t 9s = 0 + -11t Remove the zero: 9s = -11t Divide each side by '9'. s = -1.222222222t Simplifying s = -1.222222222tSolution
s = {-1t, -1.222222222t}
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