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Simplifying 5t2 = t(7t + -1) Reorder the terms: 5t2 = t(-1 + 7t) 5t2 = (-1 * t + 7t * t) 5t2 = (-1t + 7t2) Solving 5t2 = -1t + 7t2 Solving for variable 't'. Reorder the terms: t + 5t2 + -7t2 = -1t + 7t2 + t + -7t2 Combine like terms: 5t2 + -7t2 = -2t2 t + -2t2 = -1t + 7t2 + t + -7t2 Reorder the terms: t + -2t2 = -1t + t + 7t2 + -7t2 Combine like terms: -1t + t = 0 t + -2t2 = 0 + 7t2 + -7t2 t + -2t2 = 7t2 + -7t2 Combine like terms: 7t2 + -7t2 = 0 t + -2t2 = 0 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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