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Simplifying 0 = -5t2 + 10t + 40 Reorder the terms: 0 = 40 + 10t + -5t2 Solving 0 = 40 + 10t + -5t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -10t + 5t2 = 40 + 10t + -5t2 + -40 + -10t + 5t2 Reorder the terms: -40 + -10t + 5t2 = 40 + -40 + 10t + -10t + -5t2 + 5t2 Combine like terms: 40 + -40 = 0 -40 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2 -40 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2 Combine like terms: 10t + -10t = 0 -40 + -10t + 5t2 = 0 + -5t2 + 5t2 -40 + -10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -40 + -10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + -2t + t2) = 0 Factor a trinomial. 5((-2 + -1t)(4 + -1t)) = 0 Ignore the factor 5.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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-2, 4}
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