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Simplifying 0 = -16t2 + 52t + 48 Reorder the terms: 0 = 48 + 52t + -16t2 Solving 0 = 48 + 52t + -16t2 Solving for variable 't'. Combine like terms: 0 + -48 = -48 -48 + -52t + 16t2 = 48 + 52t + -16t2 + -48 + -52t + 16t2 Reorder the terms: -48 + -52t + 16t2 = 48 + -48 + 52t + -52t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 -48 + -52t + 16t2 = 0 + 52t + -52t + -16t2 + 16t2 -48 + -52t + 16t2 = 52t + -52t + -16t2 + 16t2 Combine like terms: 52t + -52t = 0 -48 + -52t + 16t2 = 0 + -16t2 + 16t2 -48 + -52t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -48 + -52t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -13t + 4t2) = 0 Factor a trinomial. 4((-3 + -4t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-0.75, 4}
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