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Simplifying 16 = -16t2 + 52t + 16 Reorder the terms: 16 = 16 + 52t + -16t2 Add '-16' to each side of the equation. 16 + -16 = 16 + 52t + -16 + -16t2 Combine like terms: 16 + -16 = 0 0 = 16 + 52t + -16 + -16t2 Reorder the terms: 0 = 16 + -16 + 52t + -16t2 Combine like terms: 16 + -16 = 0 0 = 0 + 52t + -16t2 0 = 52t + -16t2 Solving 0 = 52t + -16t2 Solving for variable 't'. Remove the zero: -52t + 16t2 = 52t + -16t2 + -52t + 16t2 Reorder the terms: -52t + 16t2 = 52t + -52t + -16t2 + 16t2 Combine like terms: 52t + -52t = 0 -52t + 16t2 = 0 + -16t2 + 16t2 -52t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -52t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-13 + 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 '(-13 + 4t)' equal to zero and attempt to solve: Simplifying -13 + 4t = 0 Solving -13 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 4t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4t = 0 + 13 4t = 0 + 13 Combine like terms: 0 + 13 = 13 4t = 13 Divide each side by '4'. t = 3.25 Simplifying t = 3.25Solution
t = {0, 3.25}
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