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Simplifying 80 = 16t2 + 64t Reorder the terms: 80 = 64t + 16t2 Solving 80 = 64t + 16t2 Solving for variable 't'. Reorder the terms: 80 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 80 + -64t + -16t2 = 0 + 16t2 + -16t2 80 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 80 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(5 + -4t + -1t2) = 0 Factor a trinomial. 16((1 + -1t)(5 + t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Solution
t = {1, -5}
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