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Simplifying 0 = -16t2 + 4t + 2 Reorder the terms: 0 = 2 + 4t + -16t2 Solving 0 = 2 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -4t + 16t2 = 2 + 4t + -16t2 + -2 + -4t + 16t2 Reorder the terms: -2 + -4t + 16t2 = 2 + -2 + 4t + -4t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -2 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -2 + -4t + 16t2 = 0 + -16t2 + 16t2 -2 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2t + 8t2) = 0 Factor a trinomial. 2((-1 + -4t)(1 + -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 '(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 = {-0.25, 0.5}
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