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Simplifying 9t2 = 24 + 30t Solving 9t2 = 24 + 30t Solving for variable 't'. Reorder the terms: -24 + -30t + 9t2 = 24 + 30t + -24 + -30t Reorder the terms: -24 + -30t + 9t2 = 24 + -24 + 30t + -30t Combine like terms: 24 + -24 = 0 -24 + -30t + 9t2 = 0 + 30t + -30t -24 + -30t + 9t2 = 30t + -30t Combine like terms: 30t + -30t = 0 -24 + -30t + 9t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -10t + 3t2) = 0 Factor a trinomial. 3((-2 + -3t)(4 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3t)' equal to zero and attempt to solve: Simplifying -2 + -3t = 0 Solving -2 + -3t = 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 + -3t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3t = 0 + 2 -3t = 0 + 2 Combine like terms: 0 + 2 = 2 -3t = 2 Divide each side by '-3'. t = -0.6666666667 Simplifying t = -0.6666666667Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-0.6666666667, 4}
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