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Simplifying 0 = -16t2 + 64t + 512 Reorder the terms: 0 = 512 + 64t + -16t2 Solving 0 = 512 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -512 = -512 -512 + -64t + 16t2 = 512 + 64t + -16t2 + -512 + -64t + 16t2 Reorder the terms: -512 + -64t + 16t2 = 512 + -512 + 64t + -64t + -16t2 + 16t2 Combine like terms: 512 + -512 = 0 -512 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -512 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -512 + -64t + 16t2 = 0 + -16t2 + 16t2 -512 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -512 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-32 + -4t + t2) = 0 Factor a trinomial. 16((-4 + -1t)(8 + -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 '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-4, 8}
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