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Simplifying -16t2 + 64t + 8 = 68 Reorder the terms: 8 + 64t + -16t2 = 68 Solving 8 + 64t + -16t2 = 68 Solving for variable 't'. Reorder the terms: 8 + -68 + 64t + -16t2 = 68 + -68 Combine like terms: 8 + -68 = -60 -60 + 64t + -16t2 = 68 + -68 Combine like terms: 68 + -68 = 0 -60 + 64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 16t + -4t2) = 0 Factor a trinomial. 4((-5 + 2t)(3 + -2t)) = 0 Ignore the factor 4.Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {2.5, 1.5}
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