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Simplifying 16t2 = 60 + 68t Solving 16t2 = 60 + 68t Solving for variable 't'. Reorder the terms: -60 + -68t + 16t2 = 60 + 68t + -60 + -68t Reorder the terms: -60 + -68t + 16t2 = 60 + -60 + 68t + -68t Combine like terms: 60 + -60 = 0 -60 + -68t + 16t2 = 0 + 68t + -68t -60 + -68t + 16t2 = 68t + -68t Combine like terms: 68t + -68t = 0 -60 + -68t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -17t + 4t2) = 0 Factor a trinomial. 4((-3 + -4t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 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 = {-0.75, 5}
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