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Simplifying 5 = 2t2 + -21t + 45 Reorder the terms: 5 = 45 + -21t + 2t2 Solving 5 = 45 + -21t + 2t2 Solving for variable 't'. Combine like terms: 5 + -45 = -40 -40 + 21t + -2t2 = 45 + -21t + 2t2 + -45 + 21t + -2t2 Reorder the terms: -40 + 21t + -2t2 = 45 + -45 + -21t + 21t + 2t2 + -2t2 Combine like terms: 45 + -45 = 0 -40 + 21t + -2t2 = 0 + -21t + 21t + 2t2 + -2t2 -40 + 21t + -2t2 = -21t + 21t + 2t2 + -2t2 Combine like terms: -21t + 21t = 0 -40 + 21t + -2t2 = 0 + 2t2 + -2t2 -40 + 21t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -40 + 21t + -2t2 = 0 Factor a trinomial. (-8 + t)(5 + -2t) = 0Subproblem 1
Set the factor '(-8 + t)' equal to zero and attempt to solve: Simplifying -8 + t = 0 Solving -8 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + t = 0 + 8 t = 0 + 8 Combine like terms: 0 + 8 = 8 t = 8 Simplifying t = 8Subproblem 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 = {8, 2.5}
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