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Simplifying 160 = -16t2 + 24t + 320 Reorder the terms: 160 = 320 + 24t + -16t2 Solving 160 = 320 + 24t + -16t2 Solving for variable 't'. Combine like terms: 160 + -320 = -160 -160 + -24t + 16t2 = 320 + 24t + -16t2 + -320 + -24t + 16t2 Reorder the terms: -160 + -24t + 16t2 = 320 + -320 + 24t + -24t + -16t2 + 16t2 Combine like terms: 320 + -320 = 0 -160 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2 -160 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 -160 + -24t + 16t2 = 0 + -16t2 + 16t2 -160 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -160 + -24t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-20 + -3t + 2t2) = 0 Factor a trinomial. 8((-5 + -2t)(4 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 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 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5Subproblem 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 = {-2.5, 4}
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