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Simplifying 0 = -16t2 + -20t + 150 Reorder the terms: 0 = 150 + -20t + -16t2 Solving 0 = 150 + -20t + -16t2 Solving for variable 't'. Combine like terms: 0 + -150 = -150 -150 + 20t + 16t2 = 150 + -20t + -16t2 + -150 + 20t + 16t2 Reorder the terms: -150 + 20t + 16t2 = 150 + -150 + -20t + 20t + -16t2 + 16t2 Combine like terms: 150 + -150 = 0 -150 + 20t + 16t2 = 0 + -20t + 20t + -16t2 + 16t2 -150 + 20t + 16t2 = -20t + 20t + -16t2 + 16t2 Combine like terms: -20t + 20t = 0 -150 + 20t + 16t2 = 0 + -16t2 + 16t2 -150 + 20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -150 + 20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 10t + 8t2) = 0 Factor a trinomial. 2((-15 + -4t)(5 + -2t)) = 0 Ignore the factor 2.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 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {-3.75, 2.5}
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