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Simplifying 0 = -16t2 + 72t + 448 Reorder the terms: 0 = 448 + 72t + -16t2 Solving 0 = 448 + 72t + -16t2 Solving for variable 't'. Combine like terms: 0 + -448 = -448 -448 + -72t + 16t2 = 448 + 72t + -16t2 + -448 + -72t + 16t2 Reorder the terms: -448 + -72t + 16t2 = 448 + -448 + 72t + -72t + -16t2 + 16t2 Combine like terms: 448 + -448 = 0 -448 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 -448 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 -448 + -72t + 16t2 = 0 + -16t2 + 16t2 -448 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -448 + -72t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-56 + -9t + 2t2) = 0 Factor a trinomial. 8((-7 + -2t)(8 + -1t)) = 0 Ignore the factor 8.Subproblem 1
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 = -3.5Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-3.5, 8}
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