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Simplifying 80t2 = 220t + 130 Reorder the terms: 80t2 = 130 + 220t Solving 80t2 = 130 + 220t Solving for variable 't'. Reorder the terms: -130 + -220t + 80t2 = 130 + 220t + -130 + -220t Reorder the terms: -130 + -220t + 80t2 = 130 + -130 + 220t + -220t Combine like terms: 130 + -130 = 0 -130 + -220t + 80t2 = 0 + 220t + -220t -130 + -220t + 80t2 = 220t + -220t Combine like terms: 220t + -220t = 0 -130 + -220t + 80t2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-13 + -22t + 8t2) = 0 Factor a trinomial. 10((-1 + -2t)(13 + -4t)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(13 + -4t)' equal to zero and attempt to solve: Simplifying 13 + -4t = 0 Solving 13 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -4t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -4t = 0 + -13 -4t = 0 + -13 Combine like terms: 0 + -13 = -13 -4t = -13 Divide each side by '-4'. t = 3.25 Simplifying t = 3.25Solution
t = {-0.5, 3.25}
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