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Simplifying 54s2 + -96st + 42t2 = 0 Reorder the terms: -96st + 54s2 + 42t2 = 0 Solving -96st + 54s2 + 42t2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '6'. 6(-16st + 9s2 + 7t2) = 0 Factor a trinomial. 6((s + -1t)(9s + -7t)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(s + -1t)' equal to zero and attempt to solve: Simplifying s + -1t = 0 Solving s + -1t = 0 Move all terms containing s to the left, all other terms to the right. Add 't' to each side of the equation. s + -1t + t = 0 + t Combine like terms: -1t + t = 0 s + 0 = 0 + t s = 0 + t Remove the zero: s = t Simplifying s = tSubproblem 2
Set the factor '(9s + -7t)' equal to zero and attempt to solve: Simplifying 9s + -7t = 0 Solving 9s + -7t = 0 Move all terms containing s to the left, all other terms to the right. Add '7t' to each side of the equation. 9s + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 9s + 0 = 0 + 7t 9s = 0 + 7t Remove the zero: 9s = 7t Divide each side by '9'. s = 0.7777777778t Simplifying s = 0.7777777778tSolution
s = {t, 0.7777777778t}
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