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Simplifying -16t2 + 48t + 160 = 0 Reorder the terms: 160 + 48t + -16t2 = 0 Solving 160 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0 Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {5, -2}
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