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Simplifying 0 = 16t2 + -52t + 12 Reorder the terms: 0 = 12 + -52t + 16t2 Solving 0 = 12 + -52t + 16t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + 52t + -16t2 = 12 + -52t + 16t2 + -12 + 52t + -16t2 Reorder the terms: -12 + 52t + -16t2 = 12 + -12 + -52t + 52t + 16t2 + -16t2 Combine like terms: 12 + -12 = 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((-3 + t)(1 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Subproblem 2
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 = 0.25Solution
t = {3, 0.25}
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