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Simplifying 3 = 3 + 75t + -16t2 Add '-3' to each side of the equation. 3 + -3 = 3 + 75t + -3 + -16t2 Combine like terms: 3 + -3 = 0 0 = 3 + 75t + -3 + -16t2 Reorder the terms: 0 = 3 + -3 + 75t + -16t2 Combine like terms: 3 + -3 = 0 0 = 0 + 75t + -16t2 0 = 75t + -16t2 Solving 0 = 75t + -16t2 Solving for variable 't'. Remove the zero: -75t + 16t2 = 75t + -16t2 + -75t + 16t2 Reorder the terms: -75t + 16t2 = 75t + -75t + -16t2 + 16t2 Combine like terms: 75t + -75t = 0 -75t + 16t2 = 0 + -16t2 + 16t2 -75t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -75t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-75 + 16t) = 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 '(-75 + 16t)' equal to zero and attempt to solve: Simplifying -75 + 16t = 0 Solving -75 + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + 16t = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 16t = 0 + 75 16t = 0 + 75 Combine like terms: 0 + 75 = 75 16t = 75 Divide each side by '16'. t = 4.6875 Simplifying t = 4.6875Solution
t = {0, 4.6875}
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