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Simplifying -40 = -2t2 + 16t Reorder the terms: -40 = 16t + -2t2 Solving -40 = 16t + -2t2 Solving for variable 't'. Reorder the terms: -40 + -16t + 2t2 = 16t + -16t + -2t2 + 2t2 Combine like terms: 16t + -16t = 0 -40 + -16t + 2t2 = 0 + -2t2 + 2t2 -40 + -16t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -40 + -16t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -8t + t2) = 0 Factor a trinomial. 2((-2 + -1t)(10 + -1t)) = 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 '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-2, 10}
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