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Simplifying t(8t + 56) = 144 Reorder the terms: t(56 + 8t) = 144 (56 * t + 8t * t) = 144 (56t + 8t2) = 144 Solving 56t + 8t2 = 144 Solving for variable 't'. Reorder the terms: -144 + 56t + 8t2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 56t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-18 + 7t + t2) = 0 Factor a trinomial. 8((-9 + -1t)(2 + -1t)) = 0 Ignore the factor 8.Subproblem 1
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 = -9Subproblem 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 = {-9, 2}
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