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Simplifying -16t2 + 8t + 224 = 0 Reorder the terms: 224 + 8t + -16t2 = 0 Solving 224 + 8t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(28 + t + -2t2) = 0 Factor a trinomial. 8((4 + -1t)(7 + 2t)) = 0 Ignore the factor 8.Subproblem 1
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 = 4Subproblem 2
Set the factor '(7 + 2t)' equal to zero and attempt to solve: Simplifying 7 + 2t = 0 Solving 7 + 2t = 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 + 2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2t = 0 + -7 2t = 0 + -7 Combine like terms: 0 + -7 = -7 2t = -7 Divide each side by '2'. t = -3.5 Simplifying t = -3.5Solution
t = {4, -3.5}
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