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Simplifying 38t + -16t2 + -22 = 0 Reorder the terms: -22 + 38t + -16t2 = 0 Solving -22 + 38t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 19t + -8t2) = 0 Factor a trinomial. 2((-11 + 8t)(1 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 8t)' equal to zero and attempt to solve: Simplifying -11 + 8t = 0 Solving -11 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 8t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 8t = 0 + 11 8t = 0 + 11 Combine like terms: 0 + 11 = 11 8t = 11 Divide each side by '8'. t = 1.375 Simplifying t = 1.375Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {1.375, 1}
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