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Simplifying t(8t + 1) = 7 Reorder the terms: t(1 + 8t) = 7 (1 * t + 8t * t) = 7 (1t + 8t2) = 7 Solving 1t + 8t2 = 7 Solving for variable 't'. Reorder the terms: -7 + 1t + 8t2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 1t + 8t2 = 0 Factor a trinomial. (-1 + -1t)(7 + -8t) = 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 '(7 + -8t)' equal to zero and attempt to solve: Simplifying 7 + -8t = 0 Solving 7 + -8t = 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 + -8t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8t = 0 + -7 -8t = 0 + -7 Combine like terms: 0 + -7 = -7 -8t = -7 Divide each side by '-8'. t = 0.875 Simplifying t = 0.875Solution
t = {-1, 0.875}
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