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Simplifying t2 + 8t = 24 + 3t Reorder the terms: 8t + t2 = 24 + 3t Solving 8t + t2 = 24 + 3t Solving for variable 't'. Reorder the terms: -24 + 8t + -3t + t2 = 24 + 3t + -24 + -3t Combine like terms: 8t + -3t = 5t -24 + 5t + t2 = 24 + 3t + -24 + -3t Reorder the terms: -24 + 5t + t2 = 24 + -24 + 3t + -3t Combine like terms: 24 + -24 = 0 -24 + 5t + t2 = 0 + 3t + -3t -24 + 5t + t2 = 3t + -3t Combine like terms: 3t + -3t = 0 -24 + 5t + t2 = 0 Factor a trinomial. (-8 + -1t)(3 + -1t) = 0Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve: Simplifying -8 + -1t = 0 Solving -8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1t = 0 + 8 -1t = 0 + 8 Combine like terms: 0 + 8 = 8 -1t = 8 Divide each side by '-1'. t = -8 Simplifying t = -8Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-8, 3}
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