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Simplifying 8 = -16t2 + 56t + 40 Reorder the terms: 8 = 40 + 56t + -16t2 Solving 8 = 40 + 56t + -16t2 Solving for variable 't'. Combine like terms: 8 + -40 = -32 -32 + -56t + 16t2 = 40 + 56t + -16t2 + -40 + -56t + 16t2 Reorder the terms: -32 + -56t + 16t2 = 40 + -40 + 56t + -56t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -32 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2 -32 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 -32 + -56t + 16t2 = 0 + -16t2 + 16t2 -32 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -32 + -56t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + -7t + 2t2) = 0 Factor a trinomial. 8((-1 + -2t)(4 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 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 = {-0.5, 4}
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