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Simplifying 84 = -16t2 + 72t + 3 Reorder the terms: 84 = 3 + 72t + -16t2 Solving 84 = 3 + 72t + -16t2 Solving for variable 't'. Combine like terms: 84 + -3 = 81 81 + -72t + 16t2 = 3 + 72t + -16t2 + -3 + -72t + 16t2 Reorder the terms: 81 + -72t + 16t2 = 3 + -3 + 72t + -72t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 81 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 81 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 81 + -72t + 16t2 = 0 + -16t2 + 16t2 81 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 81 + -72t + 16t2 = 0 Factor a trinomial. (9 + -4t)(9 + -4t) = 0Subproblem 1
Set the factor '(9 + -4t)' equal to zero and attempt to solve: Simplifying 9 + -4t = 0 Solving 9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4t = 0 + -9 -4t = 0 + -9 Combine like terms: 0 + -9 = -9 -4t = -9 Divide each side by '-4'. t = 2.25 Simplifying t = 2.25Subproblem 2
Set the factor '(9 + -4t)' equal to zero and attempt to solve: Simplifying 9 + -4t = 0 Solving 9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4t = 0 + -9 -4t = 0 + -9 Combine like terms: 0 + -9 = -9 -4t = -9 Divide each side by '-4'. t = 2.25 Simplifying t = 2.25Solution
t = {2.25, 2.25}
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