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Simplifying 0 = -16t2 + 128t + 144 Reorder the terms: 0 = 144 + 128t + -16t2 Solving 0 = 144 + 128t + -16t2 Solving for variable 't'. Combine like terms: 0 + -144 = -144 -144 + -128t + 16t2 = 144 + 128t + -16t2 + -144 + -128t + 16t2 Reorder the terms: -144 + -128t + 16t2 = 144 + -144 + 128t + -128t + -16t2 + 16t2 Combine like terms: 144 + -144 = 0 -144 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2 -144 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 -144 + -128t + 16t2 = 0 + -16t2 + 16t2 -144 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-9 + -8t + t2) = 0 Factor a trinomial. 16((-1 + -1t)(9 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 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 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-1, 9}
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