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Simplifying 0.5t * t = 0.5t(8 + -1t) Multiply t * t 0.5t2 = 0.5t(8 + -1t) 0.5t2 = (8 * 0.5t + -1t * 0.5t) 0.5t2 = (4t + -0.5t2) Solving 0.5t2 = 4t + -0.5t2 Solving for variable 't'. Reorder the terms: -4t + 0.5t2 + 0.5t2 = 4t + -0.5t2 + -4t + 0.5t2 Combine like terms: 0.5t2 + 0.5t2 = 1t2 -4t + 1t2 = 4t + -0.5t2 + -4t + 0.5t2 Reorder the terms: -4t + 1t2 = 4t + -4t + -0.5t2 + 0.5t2 Combine like terms: 4t + -4t = 0 -4t + 1t2 = 0 + -0.5t2 + 0.5t2 -4t + 1t2 = -0.5t2 + 0.5t2 Combine like terms: -0.5t2 + 0.5t2 = 0.0 -4t + 1t2 = 0.0 Factor out the Greatest Common Factor (GCF), 't'. t(-4 + t) = 0.0Subproblem 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 '(-4 + t)' equal to zero and attempt to solve: Simplifying -4 + t = 0 Solving -4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + t = 0 + 4 t = 0 + 4 Combine like terms: 0 + 4 = 4 t = 4 Simplifying t = 4Solution
t = {0, 4}
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