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Simplifying -16t2 + 1600t + -30000 = 0 Reorder the terms: -30000 + 1600t + -16t2 = 0 Solving -30000 + 1600t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-1875 + 100t + -1t2) = 0 Factor a trinomial. 16((-75 + t)(25 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-75 + t)' equal to zero and attempt to solve: Simplifying -75 + t = 0 Solving -75 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + t = 0 + 75 Combine like terms: -75 + 75 = 0 0 + t = 0 + 75 t = 0 + 75 Combine like terms: 0 + 75 = 75 t = 75 Simplifying t = 75Subproblem 2
Set the factor '(25 + -1t)' equal to zero and attempt to solve: Simplifying 25 + -1t = 0 Solving 25 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1t = 0 + -25 -1t = 0 + -25 Combine like terms: 0 + -25 = -25 -1t = -25 Divide each side by '-1'. t = 25 Simplifying t = 25Solution
t = {75, 25}
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