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Simplifying 200 = -16t2 + 112t + 20 Reorder the terms: 200 = 20 + 112t + -16t2 Solving 200 = 20 + 112t + -16t2 Solving for variable 't'. Combine like terms: 200 + -20 = 180 180 + -112t + 16t2 = 20 + 112t + -16t2 + -20 + -112t + 16t2 Reorder the terms: 180 + -112t + 16t2 = 20 + -20 + 112t + -112t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 180 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 180 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 180 + -112t + 16t2 = 0 + -16t2 + 16t2 180 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 180 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -28t + 4t2) = 0 Factor a trinomial. 4((5 + -2t)(9 + -2t)) = 0 Ignore the factor 4.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 '(9 + -2t)' equal to zero and attempt to solve: Simplifying 9 + -2t = 0 Solving 9 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2t = 0 + -9 -2t = 0 + -9 Combine like terms: 0 + -9 = -9 -2t = -9 Divide each side by '-2'. t = 4.5 Simplifying t = 4.5Solution
t = {2.5, 4.5}
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