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Simplifying -16t2 + 20t + 3 = 9 Reorder the terms: 3 + 20t + -16t2 = 9 Solving 3 + 20t + -16t2 = 9 Solving for variable 't'. Reorder the terms: 3 + -9 + 20t + -16t2 = 9 + -9 Combine like terms: 3 + -9 = -6 -6 + 20t + -16t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -6 + 20t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 10t + -8t2) = 0 Factor a trinomial. 2((-3 + 4t)(1 + -2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4t)' equal to zero and attempt to solve: Simplifying -3 + 4t = 0 Solving -3 + 4t = 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 + 4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4t = 0 + 3 4t = 0 + 3 Combine like terms: 0 + 3 = 3 4t = 3 Divide each side by '4'. t = 0.75 Simplifying t = 0.75Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 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 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Solution
t = {0.75, 0.5}
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