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Simplifying -2t[8 + -1(6 + -1t)] + 5t = 0 -2t[8 + (6 * -1 + -1t * -1)] + 5t = 0 -2t[8 + (-6 + 1t)] + 5t = 0 Combine like terms: 8 + -6 = 2 -2t[2 + 1t] + 5t = 0 [2 * -2t + 1t * -2t] + 5t = 0 [-4t + -2t2] + 5t = 0 Reorder the terms: -4t + 5t + -2t2 = 0 Combine like terms: -4t + 5t = 1t 1t + -2t2 = 0 Solving 1t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(1 + -2t) = 0Subproblem 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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