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Simplifying 400 = -16t2 + 200t Reorder the terms: 400 = 200t + -16t2 Solving 400 = 200t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -200t + 16t2 = 200t + -200t + -16t2 + 16t2 Combine like terms: 200t + -200t = 0 400 + -200t + 16t2 = 0 + -16t2 + 16t2 400 + -200t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -200t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(50 + -25t + 2t2) = 0 Factor a trinomial. 8((5 + -2t)(10 + -1t)) = 0 Ignore the factor 8.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 '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {2.5, 10}
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