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Simplifying -16t2 + 24t + 4 = 9 Reorder the terms: 4 + 24t + -16t2 = 9 Solving 4 + 24t + -16t2 = 9 Solving for variable 't'. Reorder the terms: 4 + -9 + 24t + -16t2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + 24t + -16t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + 24t + -16t2 = 0 Factor a trinomial. (-5 + 4t)(1 + -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 '(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 = 0.25Solution
t = {1.25, 0.25}
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