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Simplifying -16t2 + 64t + 512 = 512 Reorder the terms: 512 + 64t + -16t2 = 512 Add '-512' to each side of the equation. 512 + 64t + -512 + -16t2 = 512 + -512 Reorder the terms: 512 + -512 + 64t + -16t2 = 512 + -512 Combine like terms: 512 + -512 = 0 0 + 64t + -16t2 = 512 + -512 64t + -16t2 = 512 + -512 Combine like terms: 512 + -512 = 0 64t + -16t2 = 0 Solving 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16t'. 16t(4 + -1t) = 0 Ignore the factor 16.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 '(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 = 4Solution
t = {0, 4}
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