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Simplifying 6t = -16t2 + 10 Reorder the terms: 6t = 10 + -16t2 Solving 6t = 10 + -16t2 Solving for variable 't'. Reorder the terms: -10 + 6t + 16t2 = 10 + -16t2 + -10 + 16t2 Reorder the terms: -10 + 6t + 16t2 = 10 + -10 + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + 6t + 16t2 = 0 + -16t2 + 16t2 -10 + 6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + 6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 3t + 8t2) = 0 Factor a trinomial. 2((-1 + -1t)(5 + -8t)) = 0 Ignore the factor 2.Subproblem 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 '(5 + -8t)' equal to zero and attempt to solve: Simplifying 5 + -8t = 0 Solving 5 + -8t = 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 + -8t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8t = 0 + -5 -8t = 0 + -5 Combine like terms: 0 + -5 = -5 -8t = -5 Divide each side by '-8'. t = 0.625 Simplifying t = 0.625Solution
t = {-1, 0.625}
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