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Simplifying 0 = -16t2 + 20t + 300 Reorder the terms: 0 = 300 + 20t + -16t2 Solving 0 = 300 + 20t + -16t2 Solving for variable 't'. Combine like terms: 0 + -300 = -300 -300 + -20t + 16t2 = 300 + 20t + -16t2 + -300 + -20t + 16t2 Reorder the terms: -300 + -20t + 16t2 = 300 + -300 + 20t + -20t + -16t2 + 16t2 Combine like terms: 300 + -300 = 0 -300 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 -300 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 -300 + -20t + 16t2 = 0 + -16t2 + 16t2 -300 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -300 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + -5t + 4t2) = 0 Factor a trinomial. 4((-15 + -4t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -4t)' equal to zero and attempt to solve: Simplifying -15 + -4t = 0 Solving -15 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -4t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4t = 0 + 15 -4t = 0 + 15 Combine like terms: 0 + 15 = 15 -4t = 15 Divide each side by '-4'. t = -3.75 Simplifying t = -3.75Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-3.75, 5}
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