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Simplifying -16t2 + 32t + 5 = 20 Reorder the terms: 5 + 32t + -16t2 = 20 Solving 5 + 32t + -16t2 = 20 Solving for variable 't'. Reorder the terms: 5 + -20 + 32t + -16t2 = 20 + -20 Combine like terms: 5 + -20 = -15 -15 + 32t + -16t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -15 + 32t + -16t2 = 0 Factor a trinomial. (-5 + 4t)(3 + -4t) = 0Subproblem 1
Set the factor '(-5 + 4t)' equal to zero and attempt to solve: Simplifying -5 + 4t = 0 Solving -5 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4t = 0 + 5 4t = 0 + 5 Combine like terms: 0 + 5 = 5 4t = 5 Divide each side by '4'. t = 1.25 Simplifying t = 1.25Subproblem 2
Set the factor '(3 + -4t)' equal to zero and attempt to solve: Simplifying 3 + -4t = 0 Solving 3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4t = 0 + -3 -4t = 0 + -3 Combine like terms: 0 + -3 = -3 -4t = -3 Divide each side by '-4'. t = 0.75 Simplifying t = 0.75Solution
t = {1.25, 0.75}
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