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Simplifying 0 = -16t2 + -31t + 2 Reorder the terms: 0 = 2 + -31t + -16t2 Solving 0 = 2 + -31t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + 31t + 16t2 = 2 + -31t + -16t2 + -2 + 31t + 16t2 Reorder the terms: -2 + 31t + 16t2 = 2 + -2 + -31t + 31t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + 31t + 16t2 = 0 + -31t + 31t + -16t2 + 16t2 -2 + 31t + 16t2 = -31t + 31t + -16t2 + 16t2 Combine like terms: -31t + 31t = 0 -2 + 31t + 16t2 = 0 + -16t2 + 16t2 -2 + 31t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + 31t + 16t2 = 0 Factor a trinomial. (-2 + -1t)(1 + -16t) = 0Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(1 + -16t)' equal to zero and attempt to solve: Simplifying 1 + -16t = 0 Solving 1 + -16t = 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 + -16t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -16t = 0 + -1 -16t = 0 + -1 Combine like terms: 0 + -1 = -1 -16t = -1 Divide each side by '-16'. t = 0.0625 Simplifying t = 0.0625Solution
t = {-2, 0.0625}
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