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Simplifying 52 = 16t2 + 60t + -2 Reorder the terms: 52 = -2 + 60t + 16t2 Solving 52 = -2 + 60t + 16t2 Solving for variable 't'. Combine like terms: 52 + 2 = 54 54 + -60t + -16t2 = -2 + 60t + 16t2 + 2 + -60t + -16t2 Reorder the terms: 54 + -60t + -16t2 = -2 + 2 + 60t + -60t + 16t2 + -16t2 Combine like terms: -2 + 2 = 0 54 + -60t + -16t2 = 0 + 60t + -60t + 16t2 + -16t2 54 + -60t + -16t2 = 60t + -60t + 16t2 + -16t2 Combine like terms: 60t + -60t = 0 54 + -60t + -16t2 = 0 + 16t2 + -16t2 54 + -60t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 54 + -60t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -30t + -8t2) = 0 Factor a trinomial. 2((3 + -4t)(9 + 2t)) = 0 Ignore the factor 2.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 '(9 + 2t)' equal to zero and attempt to solve: Simplifying 9 + 2t = 0 Solving 9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2t = 0 + -9 2t = 0 + -9 Combine like terms: 0 + -9 = -9 2t = -9 Divide each side by '2'. t = -4.5 Simplifying t = -4.5Solution
t = {0.75, -4.5}
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