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Simplifying 16t2 + 22t + -108 = 0 Reorder the terms: -108 + 22t + 16t2 = 0 Solving -108 + 22t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 11t + 8t2) = 0 Factor a trinomial. 2((-27 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + -8t)' equal to zero and attempt to solve: Simplifying -27 + -8t = 0 Solving -27 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -8t = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -8t = 0 + 27 -8t = 0 + 27 Combine like terms: 0 + 27 = 27 -8t = 27 Divide each side by '-8'. t = -3.375 Simplifying t = -3.375Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-3.375, 2}
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