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Simplifying 0 = (-16t2) + (48t) + (160) 0 = (-16t2) + (48t) + 160 Reorder the terms: 0 = 160 + (48t) + (-16t2) Solving 0 = 160 + (48t) + (-16t2) Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + (-48t) + (16t2) = 160 + (48t) + (-16t2) + -160 + (-48t) + (16t2) Reorder the terms: -160 + (-48t) + (16t2) = 160 + -160 + (48t) + (-48t) + (-16t2) + (16t2) Combine like terms: 160 + -160 = 0 -160 + (-48t) + (16t2) = 0 + (48t) + (-48t) + (-16t2) + (16t2) -160 + (-48t) + (16t2) = (48t) + (-48t) + (-16t2) + (16t2) Combine like terms: (48t) + (-48t) = 0 -160 + (-48t) + (16t2) = 0 + (-16t2) + (16t2) -160 + (-48t) + (16t2) = (-16t2) + (16t2) Combine like terms: (-16t2) + (16t2) = 0 -160 + (-48t) + (16t2) = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-10 + (-3t) + t2) = 0 Factor a trinomial. 16((-2 + -1t)(5 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-2, 5}
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