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Simplifying 2t(8t + 5) = 84 Reorder the terms: 2t(5 + 8t) = 84 (5 * 2t + 8t * 2t) = 84 (10t + 16t2) = 84 Solving 10t + 16t2 = 84 Solving for variable 't'. Reorder the terms: -84 + 10t + 16t2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 5t + 8t2) = 0 Factor a trinomial. 2((-21 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -8t)' equal to zero and attempt to solve: Simplifying -21 + -8t = 0 Solving -21 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -8t = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -8t = 0 + 21 -8t = 0 + 21 Combine like terms: 0 + 21 = 21 -8t = 21 Divide each side by '-8'. t = -2.625 Simplifying t = -2.625Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-2.625, 2}
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