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Simplifying 392 = -16t2 + 50t + 448 Reorder the terms: 392 = 448 + 50t + -16t2 Solving 392 = 448 + 50t + -16t2 Solving for variable 't'. Combine like terms: 392 + -448 = -56 -56 + -50t + 16t2 = 448 + 50t + -16t2 + -448 + -50t + 16t2 Reorder the terms: -56 + -50t + 16t2 = 448 + -448 + 50t + -50t + -16t2 + 16t2 Combine like terms: 448 + -448 = 0 -56 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 -56 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -56 + -50t + 16t2 = 0 + -16t2 + 16t2 -56 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -56 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -25t + 8t2) = 0 Factor a trinomial. 2((-7 + -8t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -8t)' equal to zero and attempt to solve: Simplifying -7 + -8t = 0 Solving -7 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -8t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8t = 0 + 7 -8t = 0 + 7 Combine like terms: 0 + 7 = 7 -8t = 7 Divide each side by '-8'. t = -0.875 Simplifying t = -0.875Subproblem 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 = {-0.875, 4}
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