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Simplifying 0 = 16t2 + -80t + 91 Reorder the terms: 0 = 91 + -80t + 16t2 Solving 0 = 91 + -80t + 16t2 Solving for variable 't'. Combine like terms: 0 + -91 = -91 -91 + 80t + -16t2 = 91 + -80t + 16t2 + -91 + 80t + -16t2 Reorder the terms: -91 + 80t + -16t2 = 91 + -91 + -80t + 80t + 16t2 + -16t2 Combine like terms: 91 + -91 = 0 -91 + 80t + -16t2 = 0 + -80t + 80t + 16t2 + -16t2 -91 + 80t + -16t2 = -80t + 80t + 16t2 + -16t2 Combine like terms: -80t + 80t = 0 -91 + 80t + -16t2 = 0 + 16t2 + -16t2 -91 + 80t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -91 + 80t + -16t2 = 0 Factor a trinomial. (-13 + 4t)(7 + -4t) = 0Subproblem 1
Set the factor '(-13 + 4t)' equal to zero and attempt to solve: Simplifying -13 + 4t = 0 Solving -13 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 4t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4t = 0 + 13 4t = 0 + 13 Combine like terms: 0 + 13 = 13 4t = 13 Divide each side by '4'. t = 3.25 Simplifying t = 3.25Subproblem 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 = {3.25, 1.75}
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