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Simplifying -16t2 + 128t = 112 Reorder the terms: 128t + -16t2 = 112 Solving 128t + -16t2 = 112 Solving for variable 't'. Reorder the terms: -112 + 128t + -16t2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-7 + 8t + -1t2) = 0 Factor a trinomial. 16((-7 + t)(1 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Subproblem 2
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 = 1Solution
t = {7, 1}
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