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Simplifying 1600t + -16t2 = 14400 Solving 1600t + -16t2 = 14400 Solving for variable 't'. Reorder the terms: -14400 + 1600t + -16t2 = 14400 + -14400 Combine like terms: 14400 + -14400 = 0 -14400 + 1600t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-900 + 100t + -1t2) = 0 Factor a trinomial. 16((-90 + t)(10 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-90 + t)' equal to zero and attempt to solve: Simplifying -90 + t = 0 Solving -90 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + t = 0 + 90 Combine like terms: -90 + 90 = 0 0 + t = 0 + 90 t = 0 + 90 Combine like terms: 0 + 90 = 90 t = 90 Simplifying t = 90Subproblem 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 = {90, 10}
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