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Simplifying 2 + 27t + 16t2 = 12 Solving 2 + 27t + 16t2 = 12 Solving for variable 't'. Reorder the terms: 2 + -12 + 27t + 16t2 = 12 + -12 Combine like terms: 2 + -12 = -10 -10 + 27t + 16t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -10 + 27t + 16t2 = 0 Factor a trinomial. (-2 + -1t)(5 + -16t) = 0Subproblem 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 '(5 + -16t)' equal to zero and attempt to solve: Simplifying 5 + -16t = 0 Solving 5 + -16t = 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 + -16t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -16t = 0 + -5 -16t = 0 + -5 Combine like terms: 0 + -5 = -5 -16t = -5 Divide each side by '-16'. t = 0.3125 Simplifying t = 0.3125Solution
t = {-2, 0.3125}
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