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Simplifying -16t2 + 24t + 3 = 12 Reorder the terms: 3 + 24t + -16t2 = 12 Solving 3 + 24t + -16t2 = 12 Solving for variable 't'. Reorder the terms: 3 + -12 + 24t + -16t2 = 12 + -12 Combine like terms: 3 + -12 = -9 -9 + 24t + -16t2 = 12 + -12 Combine like terms: 12 + -12 = 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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