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Simplifying 16t2 + 14t + 2 = 38 Reorder the terms: 2 + 14t + 16t2 = 38 Solving 2 + 14t + 16t2 = 38 Solving for variable 't'. Reorder the terms: 2 + -38 + 14t + 16t2 = 38 + -38 Combine like terms: 2 + -38 = -36 -36 + 14t + 16t2 = 38 + -38 Combine like terms: 38 + -38 = 0 -36 + 14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 7t + 8t2) = 0 Factor a trinomial. 2((-2 + -1t)(9 + -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 '(9 + -8t)' equal to zero and attempt to solve: Simplifying 9 + -8t = 0 Solving 9 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8t = 0 + -9 -8t = 0 + -9 Combine like terms: 0 + -9 = -9 -8t = -9 Divide each side by '-8'. t = 1.125 Simplifying t = 1.125Solution
t = {-2, 1.125}
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