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Simplifying 2400 = -16t2 + 400t Reorder the terms: 2400 = 400t + -16t2 Solving 2400 = 400t + -16t2 Solving for variable 't'. Reorder the terms: 2400 + -400t + 16t2 = 400t + -400t + -16t2 + 16t2 Combine like terms: 400t + -400t = 0 2400 + -400t + 16t2 = 0 + -16t2 + 16t2 2400 + -400t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2400 + -400t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(150 + -25t + t2) = 0 Factor a trinomial. 16((10 + -1t)(15 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = 10Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15Solution
t = {10, 15}
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