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Simplifying -16t2 + 48t + 2 = 38 Reorder the terms: 2 + 48t + -16t2 = 38 Solving 2 + 48t + -16t2 = 38 Solving for variable 't'. Reorder the terms: 2 + -38 + 48t + -16t2 = 38 + -38 Combine like terms: 2 + -38 = -36 -36 + 48t + -16t2 = 38 + -38 Combine like terms: 38 + -38 = 0 -36 + 48t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + 12t + -4t2) = 0 Factor a trinomial. 4((-3 + 2t)(3 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 2t)' equal to zero and attempt to solve: Simplifying -3 + 2t = 0 Solving -3 + 2t = 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 + 2t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2t = 0 + 3 2t = 0 + 3 Combine like terms: 0 + 3 = 3 2t = 3 Divide each side by '2'. t = 1.5 Simplifying t = 1.5Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {1.5, 1.5}
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