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Simplifying 100 = -16t2 + 96t + 5 Reorder the terms: 100 = 5 + 96t + -16t2 Solving 100 = 5 + 96t + -16t2 Solving for variable 't'. Combine like terms: 100 + -5 = 95 95 + -96t + 16t2 = 5 + 96t + -16t2 + -5 + -96t + 16t2 Reorder the terms: 95 + -96t + 16t2 = 5 + -5 + 96t + -96t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 95 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 95 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 95 + -96t + 16t2 = 0 + -16t2 + 16t2 95 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 95 + -96t + 16t2 = 0 Factor a trinomial. (5 + -4t)(19 + -4t) = 0Subproblem 1
Set the factor '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 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 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Subproblem 2
Set the factor '(19 + -4t)' equal to zero and attempt to solve: Simplifying 19 + -4t = 0 Solving 19 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -4t = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -4t = 0 + -19 -4t = 0 + -19 Combine like terms: 0 + -19 = -19 -4t = -19 Divide each side by '-4'. t = 4.75 Simplifying t = 4.75Solution
t = {1.25, 4.75}
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