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Simplifying 0 = -16t2 + 96t + 640 Reorder the terms: 0 = 640 + 96t + -16t2 Solving 0 = 640 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -640 = -640 -640 + -96t + 16t2 = 640 + 96t + -16t2 + -640 + -96t + 16t2 Reorder the terms: -640 + -96t + 16t2 = 640 + -640 + 96t + -96t + -16t2 + 16t2 Combine like terms: 640 + -640 = 0 -640 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -640 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -640 + -96t + 16t2 = 0 + -16t2 + 16t2 -640 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -640 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-40 + -6t + t2) = 0 Factor a trinomial. 16((-4 + -1t)(10 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-4, 10}
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