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Simplifying -16t2 + 44t + -24 = 0 Reorder the terms: -24 + 44t + -16t2 = 0 Solving -24 + 44t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 11t + -4t2) = 0 Factor a trinomial. 4((-2 + t)(3 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + t)' equal to zero and attempt to solve: Simplifying -2 + t = 0 Solving -2 + t = 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 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2Subproblem 2
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 = 0.75Solution
t = {2, 0.75}
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