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Simplifying -16t2 + 56t + -40 = 0 Reorder the terms: -40 + 56t + -16t2 = 0 Solving -40 + 56t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 7t + -2t2) = 0 Factor a trinomial. 8((-5 + 2t)(1 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + 2t)' equal to zero and attempt to solve: Simplifying -5 + 2t = 0 Solving -5 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2t = 0 + 5 2t = 0 + 5 Combine like terms: 0 + 5 = 5 2t = 5 Divide each side by '2'. t = 2.5 Simplifying t = 2.5Subproblem 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 = {2.5, 1}
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