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Simplifying 0 = (48t2 + -70t + 25) Reorder the terms: 0 = (25 + -70t + 48t2) Remove parenthesis around (25 + -70t + 48t2) 0 = 25 + -70t + 48t2 Solving 0 = 25 + -70t + 48t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + 70t + -48t2 = 25 + -70t + 48t2 + -25 + 70t + -48t2 Reorder the terms: -25 + 70t + -48t2 = 25 + -25 + -70t + 70t + 48t2 + -48t2 Combine like terms: 25 + -25 = 0 -25 + 70t + -48t2 = 0 + -70t + 70t + 48t2 + -48t2 -25 + 70t + -48t2 = -70t + 70t + 48t2 + -48t2 Combine like terms: -70t + 70t = 0 -25 + 70t + -48t2 = 0 + 48t2 + -48t2 -25 + 70t + -48t2 = 48t2 + -48t2 Combine like terms: 48t2 + -48t2 = 0 -25 + 70t + -48t2 = 0 Factor a trinomial. (-5 + 6t)(5 + -8t) = 0Subproblem 1
Set the factor '(-5 + 6t)' equal to zero and attempt to solve: Simplifying -5 + 6t = 0 Solving -5 + 6t = 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 + 6t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6t = 0 + 5 6t = 0 + 5 Combine like terms: 0 + 5 = 5 6t = 5 Divide each side by '6'. t = 0.8333333333 Simplifying t = 0.8333333333Subproblem 2
Set the factor '(5 + -8t)' equal to zero and attempt to solve: Simplifying 5 + -8t = 0 Solving 5 + -8t = 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 + -8t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8t = 0 + -5 -8t = 0 + -5 Combine like terms: 0 + -5 = -5 -8t = -5 Divide each side by '-8'. t = 0.625 Simplifying t = 0.625Solution
t = {0.8333333333, 0.625}
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