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Simplifying 30 = -16t2 + 70t + 6 Reorder the terms: 30 = 6 + 70t + -16t2 Solving 30 = 6 + 70t + -16t2 Solving for variable 't'. Combine like terms: 30 + -6 = 24 24 + -70t + 16t2 = 6 + 70t + -16t2 + -6 + -70t + 16t2 Reorder the terms: 24 + -70t + 16t2 = 6 + -6 + 70t + -70t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 24 + -70t + 16t2 = 0 + 70t + -70t + -16t2 + 16t2 24 + -70t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 24 + -70t + 16t2 = 0 + -16t2 + 16t2 24 + -70t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 24 + -70t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -35t + 8t2) = 0 Factor a trinomial. 2((3 + -8t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -8t)' equal to zero and attempt to solve: Simplifying 3 + -8t = 0 Solving 3 + -8t = 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 + -8t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8t = 0 + -3 -8t = 0 + -3 Combine like terms: 0 + -3 = -3 -8t = -3 Divide each side by '-8'. t = 0.375 Simplifying t = 0.375Subproblem 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 = {0.375, 4}
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