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Simplifying 194 = -16t2 + 128t + 2 Reorder the terms: 194 = 2 + 128t + -16t2 Solving 194 = 2 + 128t + -16t2 Solving for variable 't'. Combine like terms: 194 + -2 = 192 192 + -128t + 16t2 = 2 + 128t + -16t2 + -2 + -128t + 16t2 Reorder the terms: 192 + -128t + 16t2 = 2 + -2 + 128t + -128t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 192 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2 192 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 192 + -128t + 16t2 = 0 + -16t2 + 16t2 192 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 192 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(12 + -8t + t2) = 0 Factor a trinomial. 16((2 + -1t)(6 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {2, 6}
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