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Simplifying 9 = -16t2 + 24t + 4 Reorder the terms: 9 = 4 + 24t + -16t2 Solving 9 = 4 + 24t + -16t2 Solving for variable 't'. Combine like terms: 9 + -4 = 5 5 + -24t + 16t2 = 4 + 24t + -16t2 + -4 + -24t + 16t2 Reorder the terms: 5 + -24t + 16t2 = 4 + -4 + 24t + -24t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 5 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2 5 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 5 + -24t + 16t2 = 0 + -16t2 + 16t2 5 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 5 + -24t + 16t2 = 0 Factor a trinomial. (1 + -4t)(5 + -4t) = 0Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 2
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 = 1.25Solution
t = {0.25, 1.25}
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