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Simplifying 100 = -16t2 + 88t + 4 Reorder the terms: 100 = 4 + 88t + -16t2 Solving 100 = 4 + 88t + -16t2 Solving for variable 't'. Combine like terms: 100 + -4 = 96 96 + -88t + 16t2 = 4 + 88t + -16t2 + -4 + -88t + 16t2 Reorder the terms: 96 + -88t + 16t2 = 4 + -4 + 88t + -88t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 96 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2 96 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2 Combine like terms: 88t + -88t = 0 96 + -88t + 16t2 = 0 + -16t2 + 16t2 96 + -88t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 96 + -88t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(12 + -11t + 2t2) = 0 Factor a trinomial. 8((3 + -2t)(4 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Subproblem 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 = {1.5, 4}
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