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Simplifying 24 = -4t2 + 10t + 24 Reorder the terms: 24 = 24 + 10t + -4t2 Add '-24' to each side of the equation. 24 + -24 = 24 + 10t + -24 + -4t2 Combine like terms: 24 + -24 = 0 0 = 24 + 10t + -24 + -4t2 Reorder the terms: 0 = 24 + -24 + 10t + -4t2 Combine like terms: 24 + -24 = 0 0 = 0 + 10t + -4t2 0 = 10t + -4t2 Solving 0 = 10t + -4t2 Solving for variable 't'. Remove the zero: -10t + 4t2 = 10t + -4t2 + -10t + 4t2 Reorder the terms: -10t + 4t2 = 10t + -10t + -4t2 + 4t2 Combine like terms: 10t + -10t = 0 -10t + 4t2 = 0 + -4t2 + 4t2 -10t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -10t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-5 + 2t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-5 + 2t)' equal to zero and attempt to solve: Simplifying -5 + 2t = 0 Solving -5 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2t = 0 + 5 2t = 0 + 5 Combine like terms: 0 + 5 = 5 2t = 5 Divide each side by '2'. t = 2.5 Simplifying t = 2.5Solution
t = {0, 2.5}
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