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Simplifying 25t + -5t2 = 20 Solving 25t + -5t2 = 20 Solving for variable 't'. Reorder the terms: -20 + 25t + -5t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 25t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 5t + -1t2) = 0 Factor a trinomial. 5((-4 + t)(1 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve: Simplifying -4 + t = 0 Solving -4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + t = 0 + 4 t = 0 + 4 Combine like terms: 0 + 4 = 4 t = 4 Simplifying t = 4Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {4, 1}
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