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