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Simplifying -16t2 + 96t + 8 = 148 Reorder the terms: 8 + 96t + -16t2 = 148 Solving 8 + 96t + -16t2 = 148 Solving for variable 't'. Reorder the terms: 8 + -148 + 96t + -16t2 = 148 + -148 Combine like terms: 8 + -148 = -140 -140 + 96t + -16t2 = 148 + -148 Combine like terms: 148 + -148 = 0 -140 + 96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + 24t + -4t2) = 0 Factor a trinomial. 4((-7 + 2t)(5 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 2t)' equal to zero and attempt to solve: Simplifying -7 + 2t = 0 Solving -7 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2t = 0 + 7 2t = 0 + 7 Combine like terms: 0 + 7 = 7 2t = 7 Divide each side by '2'. t = 3.5 Simplifying t = 3.5Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {3.5, 2.5}
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