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Simplifying 150 = -16t2 + 100t Reorder the terms: 150 = 100t + -16t2 Solving 150 = 100t + -16t2 Solving for variable 't'. Reorder the terms: 150 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 150 + -100t + 16t2 = 0 + -16t2 + 16t2 150 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 150 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -50t + 8t2) = 0 Factor a trinomial. 2((5 + -2t)(15 + -4t)) = 0 Ignore the factor 2.Subproblem 1
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 = 2.5Subproblem 2
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 = 3.75Solution
t = {2.5, 3.75}
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