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Simplifying 5 = -16t2 + 60t + 5 Reorder the terms: 5 = 5 + 60t + -16t2 Add '-5' to each side of the equation. 5 + -5 = 5 + 60t + -5 + -16t2 Combine like terms: 5 + -5 = 0 0 = 5 + 60t + -5 + -16t2 Reorder the terms: 0 = 5 + -5 + 60t + -16t2 Combine like terms: 5 + -5 = 0 0 = 0 + 60t + -16t2 0 = 60t + -16t2 Solving 0 = 60t + -16t2 Solving for variable 't'. Remove the zero: -60t + 16t2 = 60t + -16t2 + -60t + 16t2 Reorder the terms: -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 -60t + 16t2 = 0 + -16t2 + 16t2 -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-15 + 4t) = 0 Ignore the factor 4.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 '(-15 + 4t)' equal to zero and attempt to solve: Simplifying -15 + 4t = 0 Solving -15 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 4t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4t = 0 + 15 4t = 0 + 15 Combine like terms: 0 + 15 = 15 4t = 15 Divide each side by '4'. t = 3.75 Simplifying t = 3.75Solution
t = {0, 3.75}
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