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Simplifying 16 = -16t2 + 52t + 4 Reorder the terms: 16 = 4 + 52t + -16t2 Solving 16 = 4 + 52t + -16t2 Solving for variable 't'. Combine like terms: 16 + -4 = 12 12 + -52t + 16t2 = 4 + 52t + -16t2 + -4 + -52t + 16t2 Reorder the terms: 12 + -52t + 16t2 = 4 + -4 + 52t + -52t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 12 + -52t + 16t2 = 0 + 52t + -52t + -16t2 + 16t2 12 + -52t + 16t2 = 52t + -52t + -16t2 + 16t2 Combine like terms: 52t + -52t = 0 12 + -52t + 16t2 = 0 + -16t2 + 16t2 12 + -52t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 12 + -52t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -13t + 4t2) = 0 Factor a trinomial. 4((1 + -4t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {0.25, 3}
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