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Simplifying 16t2 + 16t = 1152 Reorder the terms: 16t + 16t2 = 1152 Solving 16t + 16t2 = 1152 Solving for variable 't'. Reorder the terms: -1152 + 16t + 16t2 = 1152 + -1152 Combine like terms: 1152 + -1152 = 0 -1152 + 16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-72 + t + t2) = 0 Factor a trinomial. 16((-9 + -1t)(8 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9Subproblem 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 = {-9, 8}
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