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Simplifying 12 = 2t2 + -17t + 48 Reorder the terms: 12 = 48 + -17t + 2t2 Solving 12 = 48 + -17t + 2t2 Solving for variable 't'. Combine like terms: 12 + -48 = -36 -36 + 17t + -2t2 = 48 + -17t + 2t2 + -48 + 17t + -2t2 Reorder the terms: -36 + 17t + -2t2 = 48 + -48 + -17t + 17t + 2t2 + -2t2 Combine like terms: 48 + -48 = 0 -36 + 17t + -2t2 = 0 + -17t + 17t + 2t2 + -2t2 -36 + 17t + -2t2 = -17t + 17t + 2t2 + -2t2 Combine like terms: -17t + 17t = 0 -36 + 17t + -2t2 = 0 + 2t2 + -2t2 -36 + 17t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -36 + 17t + -2t2 = 0 Factor a trinomial. (-9 + 2t)(4 + -1t) = 0Subproblem 1
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 = 4.5Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {4.5, 4}
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