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Simplifying 1750 + 900t + -250t2 = 0 Solving 1750 + 900t + -250t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '50'. 50(35 + 18t + -5t2) = 0 Factor a trinomial. 50((5 + -1t)(7 + 5t)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Subproblem 2
Set the factor '(7 + 5t)' equal to zero and attempt to solve: Simplifying 7 + 5t = 0 Solving 7 + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5t = 0 + -7 5t = 0 + -7 Combine like terms: 0 + -7 = -7 5t = -7 Divide each side by '5'. t = -1.4 Simplifying t = -1.4Solution
t = {5, -1.4}
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