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Simplifying 104 = -16t2 + 80t + 200 Reorder the terms: 104 = 200 + 80t + -16t2 Solving 104 = 200 + 80t + -16t2 Solving for variable 't'. Combine like terms: 104 + -200 = -96 -96 + -80t + 16t2 = 200 + 80t + -16t2 + -200 + -80t + 16t2 Reorder the terms: -96 + -80t + 16t2 = 200 + -200 + 80t + -80t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -96 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 -96 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 -96 + -80t + 16t2 = 0 + -16t2 + 16t2 -96 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -96 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-6 + -5t + t2) = 0 Factor a trinomial. 16((-1 + -1t)(6 + -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 '(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 = {-1, 6}
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