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Simplifying 0 = 45 + 4t + -1t2 Solving 0 = 45 + 4t + -1t2 Solving for variable 't'. Combine like terms: 0 + -45 = -45 -45 + -4t + t2 = 45 + 4t + -1t2 + -45 + -4t + t2 Reorder the terms: -45 + -4t + t2 = 45 + -45 + 4t + -4t + -1t2 + t2 Combine like terms: 45 + -45 = 0 -45 + -4t + t2 = 0 + 4t + -4t + -1t2 + t2 -45 + -4t + t2 = 4t + -4t + -1t2 + t2 Combine like terms: 4t + -4t = 0 -45 + -4t + t2 = 0 + -1t2 + t2 -45 + -4t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -45 + -4t + t2 = 0 Factor a trinomial. (-5 + -1t)(9 + -1t) = 0Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 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 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-5, 9}
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