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Simplifying 576 = 208t + -16t2 Solving 576 = 208t + -16t2 Solving for variable 't'. Reorder the terms: 576 + -208t + 16t2 = 208t + -208t + -16t2 + 16t2 Combine like terms: 208t + -208t = 0 576 + -208t + 16t2 = 0 + -16t2 + 16t2 576 + -208t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 576 + -208t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(36 + -13t + t2) = 0 Factor a trinomial. 16((4 + -1t)(9 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = 4Subproblem 2
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 = 9Solution
t = {4, 9}
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