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Simplifying 0 = -16t2 + -9t + 46 Reorder the terms: 0 = 46 + -9t + -16t2 Solving 0 = 46 + -9t + -16t2 Solving for variable 't'. Combine like terms: 0 + -46 = -46 -46 + 9t + 16t2 = 46 + -9t + -16t2 + -46 + 9t + 16t2 Reorder the terms: -46 + 9t + 16t2 = 46 + -46 + -9t + 9t + -16t2 + 16t2 Combine like terms: 46 + -46 = 0 -46 + 9t + 16t2 = 0 + -9t + 9t + -16t2 + 16t2 -46 + 9t + 16t2 = -9t + 9t + -16t2 + 16t2 Combine like terms: -9t + 9t = 0 -46 + 9t + 16t2 = 0 + -16t2 + 16t2 -46 + 9t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -46 + 9t + 16t2 = 0 Factor a trinomial. (-2 + -1t)(23 + -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 '(23 + -16t)' equal to zero and attempt to solve: Simplifying 23 + -16t = 0 Solving 23 + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -16t = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -16t = 0 + -23 -16t = 0 + -23 Combine like terms: 0 + -23 = -23 -16t = -23 Divide each side by '-16'. t = 1.4375 Simplifying t = 1.4375Solution
t = {-2, 1.4375}
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