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Simplifying -8t2 + 8t + 30 = 0 Reorder the terms: 30 + 8t + -8t2 = 0 Solving 30 + 8t + -8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 4t + -4t2) = 0 Factor a trinomial. 2((5 + -2t)(3 + 2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve: Simplifying 3 + 2t = 0 Solving 3 + 2t = 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 + 2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2t = 0 + -3 2t = 0 + -3 Combine like terms: 0 + -3 = -3 2t = -3 Divide each side by '2'. t = -1.5 Simplifying t = -1.5Solution
t = {2.5, -1.5}
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