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Simplifying 320 = 144t + -16t2 Solving 320 = 144t + -16t2 Solving for variable 't'. Reorder the terms: 320 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 320 + -144t + 16t2 = 0 + -16t2 + 16t2 320 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 320 + -144t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(20 + -9t + t2) = 0 Factor a trinomial. 16((4 + -1t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {4, 5}
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