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Simplifying 2(t) = 64t + -64t2 Solving 2t = 64t + -64t2 Solving for variable 't'. Combine like terms: 2t + -64t = -62t -62t + 64t2 = 64t + -64t2 + -64t + 64t2 Reorder the terms: -62t + 64t2 = 64t + -64t + -64t2 + 64t2 Combine like terms: 64t + -64t = 0 -62t + 64t2 = 0 + -64t2 + 64t2 -62t + 64t2 = -64t2 + 64t2 Combine like terms: -64t2 + 64t2 = 0 -62t + 64t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-31 + 32t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-31 + 32t)' equal to zero and attempt to solve: Simplifying -31 + 32t = 0 Solving -31 + 32t = 0 Move all terms containing t to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + 32t = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 32t = 0 + 31 32t = 0 + 31 Combine like terms: 0 + 31 = 31 32t = 31 Divide each side by '32'. t = 0.96875 Simplifying t = 0.96875Solution
t = {0, 0.96875}
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