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Simplifying t(10t + 1) = 9 Reorder the terms: t(1 + 10t) = 9 (1 * t + 10t * t) = 9 (1t + 10t2) = 9 Solving 1t + 10t2 = 9 Solving for variable 't'. Reorder the terms: -9 + 1t + 10t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 1t + 10t2 = 0 Factor a trinomial. (-1 + -1t)(9 + -10t) = 0Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 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 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
Set the factor '(9 + -10t)' equal to zero and attempt to solve: Simplifying 9 + -10t = 0 Solving 9 + -10t = 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 + -10t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10t = 0 + -9 -10t = 0 + -9 Combine like terms: 0 + -9 = -9 -10t = -9 Divide each side by '-10'. t = 0.9 Simplifying t = 0.9Solution
t = {-1, 0.9}
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