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Simplifying 0 = 16t2 + 96t + 80 Reorder the terms: 0 = 80 + 96t + 16t2 Solving 0 = 80 + 96t + 16t2 Solving for variable 't'. Combine like terms: 0 + -80 = -80 -80 + -96t + -16t2 = 80 + 96t + 16t2 + -80 + -96t + -16t2 Reorder the terms: -80 + -96t + -16t2 = 80 + -80 + 96t + -96t + 16t2 + -16t2 Combine like terms: 80 + -80 = 0 -80 + -96t + -16t2 = 0 + 96t + -96t + 16t2 + -16t2 -80 + -96t + -16t2 = 96t + -96t + 16t2 + -16t2 Combine like terms: 96t + -96t = 0 -80 + -96t + -16t2 = 0 + 16t2 + -16t2 -80 + -96t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -80 + -96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(5 + 6t + t2) = 0 Factor a trinomial. -16((5 + t)(1 + t)) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {-5, -1}
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