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Simplifying -16t2 + 96t + 4 = 112 Reorder the terms: 4 + 96t + -16t2 = 112 Solving 4 + 96t + -16t2 = 112 Solving for variable 't'. Reorder the terms: 4 + -112 + 96t + -16t2 = 112 + -112 Combine like terms: 4 + -112 = -108 -108 + 96t + -16t2 = 112 + -112 Combine like terms: 112 + -112 = 0 -108 + 96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + 24t + -4t2) = 0 Factor a trinomial. 4((-9 + 2t)(3 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + 2t)' equal to zero and attempt to solve: Simplifying -9 + 2t = 0 Solving -9 + 2t = 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 + 2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t = 0 + 9 2t = 0 + 9 Combine like terms: 0 + 9 = 9 2t = 9 Divide each side by '2'. t = 4.5 Simplifying t = 4.5Subproblem 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 = {4.5, 1.5}
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