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Simplifying 0 = -16t2 + 24t + -9 Reorder the terms: 0 = -9 + 24t + -16t2 Solving 0 = -9 + 24t + -16t2 Solving for variable 't'. Combine like terms: 0 + 9 = 9 9 + -24t + 16t2 = -9 + 24t + -16t2 + 9 + -24t + 16t2 Reorder the terms: 9 + -24t + 16t2 = -9 + 9 + 24t + -24t + -16t2 + 16t2 Combine like terms: -9 + 9 = 0 9 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2 9 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 9 + -24t + 16t2 = 0 + -16t2 + 16t2 9 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 9 + -24t + 16t2 = 0 Factor a trinomial. (3 + -4t)(3 + -4t) = 0Subproblem 1
Set the factor '(3 + -4t)' equal to zero and attempt to solve: Simplifying 3 + -4t = 0 Solving 3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4t = 0 + -3 -4t = 0 + -3 Combine like terms: 0 + -3 = -3 -4t = -3 Divide each side by '-4'. t = 0.75 Simplifying t = 0.75Subproblem 2
Set the factor '(3 + -4t)' equal to zero and attempt to solve: Simplifying 3 + -4t = 0 Solving 3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4t = 0 + -3 -4t = 0 + -3 Combine like terms: 0 + -3 = -3 -4t = -3 Divide each side by '-4'. t = 0.75 Simplifying t = 0.75Solution
t = {0.75, 0.75}
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