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Simplifying (5t2 + -9t + 1) + -1(8t + 13) = 0 Reorder the terms: (1 + -9t + 5t2) + -1(8t + 13) = 0 Remove parenthesis around (1 + -9t + 5t2) 1 + -9t + 5t2 + -1(8t + 13) = 0 Reorder the terms: 1 + -9t + 5t2 + -1(13 + 8t) = 0 1 + -9t + 5t2 + (13 * -1 + 8t * -1) = 0 1 + -9t + 5t2 + (-13 + -8t) = 0 Reorder the terms: 1 + -13 + -9t + -8t + 5t2 = 0 Combine like terms: 1 + -13 = -12 -12 + -9t + -8t + 5t2 = 0 Combine like terms: -9t + -8t = -17t -12 + -17t + 5t2 = 0 Solving -12 + -17t + 5t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -5t)(4 + -1t) = 0Subproblem 1
Set the factor '(-3 + -5t)' equal to zero and attempt to solve: Simplifying -3 + -5t = 0 Solving -3 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5t = 0 + 3 -5t = 0 + 3 Combine like terms: 0 + 3 = 3 -5t = 3 Divide each side by '-5'. t = -0.6 Simplifying t = -0.6Subproblem 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 = {-0.6, 4}
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