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Simplifying -16t2 + 64t + 512 = 0 Reorder the terms: 512 + 64t + -16t2 = 0 Solving 512 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(32 + 4t + -1t2) = 0 Factor a trinomial. 16((8 + -1t)(4 + t)) = 0 Ignore the factor 16.Subproblem 1
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 = 8Subproblem 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 = {8, -4}
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