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Simplifying 325 = 90t + -5t2 Solving 325 = 90t + -5t2 Solving for variable 't'. Reorder the terms: 325 + -90t + 5t2 = 90t + -90t + -5t2 + 5t2 Combine like terms: 90t + -90t = 0 325 + -90t + 5t2 = 0 + -5t2 + 5t2 325 + -90t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 325 + -90t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(65 + -18t + t2) = 0 Factor a trinomial. 5((5 + -1t)(13 + -1t)) = 0 Ignore the factor 5.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 '(13 + -1t)' equal to zero and attempt to solve: Simplifying 13 + -1t = 0 Solving 13 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1t = 0 + -13 -1t = 0 + -13 Combine like terms: 0 + -13 = -13 -1t = -13 Divide each side by '-1'. t = 13 Simplifying t = 13Solution
t = {5, 13}
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