Question
Ashlee Lange Solve for \( t \). Separate multiple answers with a comma. \[ 24 t^{2}+33 t=9 t \] \( t= \)
Ask by Floyd Lowe. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( t = 0, -1 \)
Solution
Start with the equation:
24t² + 33t = 9t
Subtract 9t from both sides:
24t² + 33t - 9t = 0
24t² + 24t = 0
Factor out 24t:
24t(t + 1) = 0
Set each factor equal to zero:
1. 24t = 0 ⟹ t = 0
2. t + 1 = 0 ⟹ t = -1
Thus, the solutions are:
t = 0, -1
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Simplify this solution The Deep Dive
To solve for \( t \), let's first rearrange the equation. Start by bringing all terms to one side: \[ 24t^2 + 33t - 9t = 0 \] This simplifies to: \[ 24t^2 + 24t = 0 \] Next, we can factor out the common term: \[ 24t(t + 1) = 0 \] Now, set each factor equal to zero: 1. \( 24t = 0 \) gives \( t = 0 \) 2. \( t + 1 = 0 \) gives \( t = -1 \) So the solutions are: \( t = 0, -1 \)
