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Simplifying 5.5 = -16t2 + 40t + 5.5 Reorder the terms: 5.5 = 5.5 + 40t + -16t2 Add '-5.5' to each side of the equation. 5.5 + -5.5 = 5.5 + 40t + -5.5 + -16t2 Combine like terms: 5.5 + -5.5 = 0.0 0.0 = 5.5 + 40t + -5.5 + -16t2 Reorder the terms: 0.0 = 5.5 + -5.5 + 40t + -16t2 Combine like terms: 5.5 + -5.5 = 0.0 0.0 = 0.0 + 40t + -16t2 0.0 = 40t + -16t2 Solving 0.0 = 40t + -16t2 Solving for variable 't'. Remove the zero: -40t + 16t2 = 40t + -16t2 + -40t + 16t2 Reorder the terms: -40t + 16t2 = 40t + -40t + -16t2 + 16t2 Combine like terms: 40t + -40t = 0 -40t + 16t2 = 0 + -16t2 + 16t2 -40t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(-5 + 2t) = 0 Ignore the factor 8.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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