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Simplifying 15 = -16t2 + 44t + 5 Reorder the terms: 15 = 5 + 44t + -16t2 Solving 15 = 5 + 44t + -16t2 Solving for variable 't'. Combine like terms: 15 + -5 = 10 10 + -44t + 16t2 = 5 + 44t + -16t2 + -5 + -44t + 16t2 Reorder the terms: 10 + -44t + 16t2 = 5 + -5 + 44t + -44t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 10 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 10 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 10 + -44t + 16t2 = 0 + -16t2 + 16t2 10 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -22t + 8t2) = 0 Factor a trinomial. 2((1 + -4t)(5 + -2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {0.25, 2.5}
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