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Simplifying 0 = 25t2 + -30t + 9 Reorder the terms: 0 = 9 + -30t + 25t2 Solving 0 = 9 + -30t + 25t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + 30t + -25t2 = 9 + -30t + 25t2 + -9 + 30t + -25t2 Reorder the terms: -9 + 30t + -25t2 = 9 + -9 + -30t + 30t + 25t2 + -25t2 Combine like terms: 9 + -9 = 0 -9 + 30t + -25t2 = 0 + -30t + 30t + 25t2 + -25t2 -9 + 30t + -25t2 = -30t + 30t + 25t2 + -25t2 Combine like terms: -30t + 30t = 0 -9 + 30t + -25t2 = 0 + 25t2 + -25t2 -9 + 30t + -25t2 = 25t2 + -25t2 Combine like terms: 25t2 + -25t2 = 0 -9 + 30t + -25t2 = 0 Factor a trinomial. (-3 + 5t)(3 + -5t) = 0Subproblem 1
Set the factor '(-3 + 5t)' equal to zero and attempt to solve: Simplifying -3 + 5t = 0 Solving -3 + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 5t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5t = 0 + 3 5t = 0 + 3 Combine like terms: 0 + 3 = 3 5t = 3 Divide each side by '5'. t = 0.6 Simplifying t = 0.6Subproblem 2
Set the factor '(3 + -5t)' equal to zero and attempt to solve: Simplifying 3 + -5t = 0 Solving 3 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5t = 0 + -3 -5t = 0 + -3 Combine like terms: 0 + -3 = -3 -5t = -3 Divide each side by '-5'. t = 0.6 Simplifying t = 0.6Solution
t = {0.6, 0.6}
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