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Simplifying 0 = 16t2 + 10t + -84 Reorder the terms: 0 = -84 + 10t + 16t2 Solving 0 = -84 + 10t + 16t2 Solving for variable 't'. Combine like terms: 0 + 84 = 84 84 + -10t + -16t2 = -84 + 10t + 16t2 + 84 + -10t + -16t2 Reorder the terms: 84 + -10t + -16t2 = -84 + 84 + 10t + -10t + 16t2 + -16t2 Combine like terms: -84 + 84 = 0 84 + -10t + -16t2 = 0 + 10t + -10t + 16t2 + -16t2 84 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2 Combine like terms: 10t + -10t = 0 84 + -10t + -16t2 = 0 + 16t2 + -16t2 84 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 84 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -5t + -8t2) = 0 Factor a trinomial. 2((2 + -1t)(21 + 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 '(21 + 8t)' equal to zero and attempt to solve: Simplifying 21 + 8t = 0 Solving 21 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 8t = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 8t = 0 + -21 8t = 0 + -21 Combine like terms: 0 + -21 = -21 8t = -21 Divide each side by '8'. t = -2.625 Simplifying t = -2.625Solution
t = {2, -2.625}
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