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Simplifying 75t = 175t(t + -4) Reorder the terms: 75t = 175t(-4 + t) 75t = (-4 * 175t + t * 175t) 75t = (-700t + 175t2) Solving 75t = -700t + 175t2 Solving for variable 't'. Combine like terms: 75t + 700t = 775t 775t + -175t2 = -700t + 175t2 + 700t + -175t2 Reorder the terms: 775t + -175t2 = -700t + 700t + 175t2 + -175t2 Combine like terms: -700t + 700t = 0 775t + -175t2 = 0 + 175t2 + -175t2 775t + -175t2 = 175t2 + -175t2 Combine like terms: 175t2 + -175t2 = 0 775t + -175t2 = 0 Factor out the Greatest Common Factor (GCF), '25t'. 25t(31 + -7t) = 0 Ignore the factor 25.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 '(31 + -7t)' equal to zero and attempt to solve: Simplifying 31 + -7t = 0 Solving 31 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -7t = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -7t = 0 + -31 -7t = 0 + -31 Combine like terms: 0 + -31 = -31 -7t = -31 Divide each side by '-7'. t = 4.428571429 Simplifying t = 4.428571429Solution
t = {0, 4.428571429}
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