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Simplifying 0 = -16t2 + 44t + -24 Reorder the terms: 0 = -24 + 44t + -16t2 Solving 0 = -24 + 44t + -16t2 Solving for variable 't'. Combine like terms: 0 + 24 = 24 24 + -44t + 16t2 = -24 + 44t + -16t2 + 24 + -44t + 16t2 Reorder the terms: 24 + -44t + 16t2 = -24 + 24 + 44t + -44t + -16t2 + 16t2 Combine like terms: -24 + 24 = 0 24 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 24 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 24 + -44t + 16t2 = 0 + -16t2 + 16t2 24 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 24 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -11t + 4t2) = 0 Factor a trinomial. 4((3 + -4t)(2 + -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 '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0.75, 2}
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