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Simplifying 40 = 8t(7 + -2t) 40 = (7 * 8t + -2t * 8t) 40 = (56t + -16t2) Solving 40 = 56t + -16t2 Solving for variable 't'. Reorder the terms: 40 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 40 + -56t + 16t2 = 0 + -16t2 + 16t2 40 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 40 + -56t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(5 + -7t + 2t2) = 0 Factor a trinomial. 8((1 + -1t)(5 + -2t)) = 0 Ignore the factor 8.Subproblem 1
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 = 1Subproblem 2
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 = 2.5Solution
t = {1, 2.5}
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