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Simplifying 16t2 + 80t + 100 = 0 Reorder the terms: 100 + 80t + 16t2 = 0 Solving 100 + 80t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 20t + 4t2) = 0 Factor a trinomial. 4((5 + 2t)(5 + 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 '(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 = {-2.5, -2.5}
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