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Simplifying -16t2 + -192t = 512 Reorder the terms: -192t + -16t2 = 512 Solving -192t + -16t2 = 512 Solving for variable 't'. Reorder the terms: -512 + -192t + -16t2 = 512 + -512 Combine like terms: 512 + -512 = 0 -512 + -192t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(32 + 12t + t2) = 0 Factor a trinomial. -16((8 + t)(4 + t)) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(8 + t)' equal to zero and attempt to solve: Simplifying 8 + t = 0 Solving 8 + t = 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 + t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + t = 0 + -8 t = 0 + -8 Combine like terms: 0 + -8 = -8 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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