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Simplifying 200 = 16t2 + 50t + 200 Reorder the terms: 200 = 200 + 50t + 16t2 Add '-200' to each side of the equation. 200 + -200 = 200 + 50t + -200 + 16t2 Combine like terms: 200 + -200 = 0 0 = 200 + 50t + -200 + 16t2 Reorder the terms: 0 = 200 + -200 + 50t + 16t2 Combine like terms: 200 + -200 = 0 0 = 0 + 50t + 16t2 0 = 50t + 16t2 Solving 0 = 50t + 16t2 Solving for variable 't'. Remove the zero: -50t + -16t2 = 50t + 16t2 + -50t + -16t2 Reorder the terms: -50t + -16t2 = 50t + -50t + 16t2 + -16t2 Combine like terms: 50t + -50t = 0 -50t + -16t2 = 0 + 16t2 + -16t2 -50t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -50t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2t'. -2t(25 + 8t) = 0 Ignore the factor -2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(25 + 8t)' equal to zero and attempt to solve: Simplifying 25 + 8t = 0 Solving 25 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 8t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 8t = 0 + -25 8t = 0 + -25 Combine like terms: 0 + -25 = -25 8t = -25 Divide each side by '8'. t = -3.125 Simplifying t = -3.125Solution
t = {0, -3.125}
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