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