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Simplifying 540 = -16t2 + 192t Reorder the terms: 540 = 192t + -16t2 Solving 540 = 192t + -16t2 Solving for variable 't'. Reorder the terms: 540 + -192t + 16t2 = 192t + -192t + -16t2 + 16t2 Combine like terms: 192t + -192t = 0 540 + -192t + 16t2 = 0 + -16t2 + 16t2 540 + -192t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 540 + -192t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(135 + -48t + 4t2) = 0 Factor a trinomial. 4((9 + -2t)(15 + -2t)) = 0 Ignore the factor 4.Subproblem 1
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 = 4.5Subproblem 2
Set the factor '(15 + -2t)' equal to zero and attempt to solve: Simplifying 15 + -2t = 0 Solving 15 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2t = 0 + -15 -2t = 0 + -15 Combine like terms: 0 + -15 = -15 -2t = -15 Divide each side by '-2'. t = 7.5 Simplifying t = 7.5Solution
t = {4.5, 7.5}
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