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Simplifying 0 = -16t2 + 24t + 7 Reorder the terms: 0 = 7 + 24t + -16t2 Solving 0 = 7 + 24t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + -24t + 16t2 = 7 + 24t + -16t2 + -7 + -24t + 16t2 Reorder the terms: -7 + -24t + 16t2 = 7 + -7 + 24t + -24t + -16t2 + 16t2 Combine like terms: 7 + -7 = 0 -7 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2 -7 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 -7 + -24t + 16t2 = 0 + -16t2 + 16t2 -7 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + -24t + 16t2 = 0 Factor a trinomial. (-1 + -4t)(7 + -4t) = 0Subproblem 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 '(7 + -4t)' equal to zero and attempt to solve: Simplifying 7 + -4t = 0 Solving 7 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t = 0 + -7 -4t = 0 + -7 Combine like terms: 0 + -7 = -7 -4t = -7 Divide each side by '-4'. t = 1.75 Simplifying t = 1.75Solution
t = {-0.25, 1.75}
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