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Simplifying 80 = 8t + 16t2 Solving 80 = 8t + 16t2 Solving for variable 't'. Reorder the terms: 80 + -8t + -16t2 = 8t + -8t + 16t2 + -16t2 Combine like terms: 8t + -8t = 0 80 + -8t + -16t2 = 0 + 16t2 + -16t2 80 + -8t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 80 + -8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(10 + -1t + -2t2) = 0 Factor a trinomial. 8((2 + -1t)(5 + 2t)) = 0 Ignore the factor 8.Subproblem 1
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 = 2Subproblem 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 = {2, -2.5}
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