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Simplifying 0 = 9t2 + -10t + 1 Reorder the terms: 0 = 1 + -10t + 9t2 Solving 0 = 1 + -10t + 9t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + 10t + -9t2 = 1 + -10t + 9t2 + -1 + 10t + -9t2 Reorder the terms: -1 + 10t + -9t2 = 1 + -1 + -10t + 10t + 9t2 + -9t2 Combine like terms: 1 + -1 = 0 -1 + 10t + -9t2 = 0 + -10t + 10t + 9t2 + -9t2 -1 + 10t + -9t2 = -10t + 10t + 9t2 + -9t2 Combine like terms: -10t + 10t = 0 -1 + 10t + -9t2 = 0 + 9t2 + -9t2 -1 + 10t + -9t2 = 9t2 + -9t2 Combine like terms: 9t2 + -9t2 = 0 -1 + 10t + -9t2 = 0 Factor a trinomial. (-1 + t)(1 + -9t) = 0Subproblem 1
Set the factor '(-1 + t)' equal to zero and attempt to solve: Simplifying -1 + t = 0 Solving -1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0 + 1 t = 0 + 1 Combine like terms: 0 + 1 = 1 t = 1 Simplifying t = 1Subproblem 2
Set the factor '(1 + -9t)' equal to zero and attempt to solve: Simplifying 1 + -9t = 0 Solving 1 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -9t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9t = 0 + -1 -9t = 0 + -1 Combine like terms: 0 + -1 = -1 -9t = -1 Divide each side by '-9'. t = 0.1111111111 Simplifying t = 0.1111111111Solution
t = {1, 0.1111111111}
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