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Simplifying 126 = -16t2 + 42t + 144 Reorder the terms: 126 = 144 + 42t + -16t2 Solving 126 = 144 + 42t + -16t2 Solving for variable 't'. Combine like terms: 126 + -144 = -18 -18 + -42t + 16t2 = 144 + 42t + -16t2 + -144 + -42t + 16t2 Reorder the terms: -18 + -42t + 16t2 = 144 + -144 + 42t + -42t + -16t2 + 16t2 Combine like terms: 144 + -144 = 0 -18 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 -18 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 -18 + -42t + 16t2 = 0 + -16t2 + 16t2 -18 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + -42t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -21t + 8t2) = 0 Factor a trinomial. 2((-3 + -8t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8t)' equal to zero and attempt to solve: Simplifying -3 + -8t = 0 Solving -3 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -8t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8t = 0 + 3 -8t = 0 + 3 Combine like terms: 0 + 3 = 3 -8t = 3 Divide each side by '-8'. t = -0.375 Simplifying t = -0.375Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.375, 3}
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