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Simplifying 32 = -16t2 + 42t + 6 Reorder the terms: 32 = 6 + 42t + -16t2 Solving 32 = 6 + 42t + -16t2 Solving for variable 't'. Combine like terms: 32 + -6 = 26 26 + -42t + 16t2 = 6 + 42t + -16t2 + -6 + -42t + 16t2 Reorder the terms: 26 + -42t + 16t2 = 6 + -6 + 42t + -42t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 26 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 26 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 26 + -42t + 16t2 = 0 + -16t2 + 16t2 26 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 26 + -42t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -21t + 8t2) = 0 Factor a trinomial. 2((1 + -1t)(13 + -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 '(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 = {1, 1.625}
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