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Simplifying 8t2 = 18 + 18t Solving 8t2 = 18 + 18t Solving for variable 't'. Reorder the terms: -18 + -18t + 8t2 = 18 + 18t + -18 + -18t Reorder the terms: -18 + -18t + 8t2 = 18 + -18 + 18t + -18t Combine like terms: 18 + -18 = 0 -18 + -18t + 8t2 = 0 + 18t + -18t -18 + -18t + 8t2 = 18t + -18t Combine like terms: 18t + -18t = 0 -18 + -18t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -9t + 4t2) = 0 Factor a trinomial. 2((-3 + -4t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.75, 3}
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