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Simplifying 224 = -16t2 + 8t + 224 Reorder the terms: 224 = 224 + 8t + -16t2 Add '-224' to each side of the equation. 224 + -224 = 224 + 8t + -224 + -16t2 Combine like terms: 224 + -224 = 0 0 = 224 + 8t + -224 + -16t2 Reorder the terms: 0 = 224 + -224 + 8t + -16t2 Combine like terms: 224 + -224 = 0 0 = 0 + 8t + -16t2 0 = 8t + -16t2 Solving 0 = 8t + -16t2 Solving for variable 't'. Remove the zero: -8t + 16t2 = 8t + -16t2 + -8t + 16t2 Reorder the terms: -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -8t + 16t2 = 0 + -16t2 + 16t2 -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(-1 + 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 '(-1 + 2t)' equal to zero and attempt to solve: Simplifying -1 + 2t = 0 Solving -1 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2t = 0 + 1 2t = 0 + 1 Combine like terms: 0 + 1 = 1 2t = 1 Divide each side by '2'. t = 0.5 Simplifying t = 0.5Solution
t = {0, 0.5}
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