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Simplifying 6 = 2t2 + -25t + 69 Reorder the terms: 6 = 69 + -25t + 2t2 Solving 6 = 69 + -25t + 2t2 Solving for variable 't'. Combine like terms: 6 + -69 = -63 -63 + 25t + -2t2 = 69 + -25t + 2t2 + -69 + 25t + -2t2 Reorder the terms: -63 + 25t + -2t2 = 69 + -69 + -25t + 25t + 2t2 + -2t2 Combine like terms: 69 + -69 = 0 -63 + 25t + -2t2 = 0 + -25t + 25t + 2t2 + -2t2 -63 + 25t + -2t2 = -25t + 25t + 2t2 + -2t2 Combine like terms: -25t + 25t = 0 -63 + 25t + -2t2 = 0 + 2t2 + -2t2 -63 + 25t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -63 + 25t + -2t2 = 0 Factor a trinomial. (-9 + t)(7 + -2t) = 0Subproblem 1
Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 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 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {9, 3.5}
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