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Simplifying -16t2 + 6t = -52 Reorder the terms: 6t + -16t2 = -52 Solving 6t + -16t2 = -52 Solving for variable 't'. Reorder the terms: 52 + 6t + -16t2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 6t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 3t + -8t2) = 0 Factor a trinomial. 2((2 + -1t)(13 + 8t)) = 0 Ignore the factor 2.Subproblem 1
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 = 2Subproblem 2
Set the factor '(13 + 8t)' equal to zero and attempt to solve: Simplifying 13 + 8t = 0 Solving 13 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 8t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 8t = 0 + -13 8t = 0 + -13 Combine like terms: 0 + -13 = -13 8t = -13 Divide each side by '8'. t = -1.625 Simplifying t = -1.625Solution
t = {2, -1.625}
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