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Simplifying 345 = 130t + -5t2 Solving 345 = 130t + -5t2 Solving for variable 't'. Reorder the terms: 345 + -130t + 5t2 = 130t + -130t + -5t2 + 5t2 Combine like terms: 130t + -130t = 0 345 + -130t + 5t2 = 0 + -5t2 + 5t2 345 + -130t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 345 + -130t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(69 + -26t + t2) = 0 Factor a trinomial. 5((3 + -1t)(23 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(23 + -1t)' equal to zero and attempt to solve: Simplifying 23 + -1t = 0 Solving 23 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -1t = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -1t = 0 + -23 -1t = 0 + -23 Combine like terms: 0 + -23 = -23 -1t = -23 Divide each side by '-1'. t = 23 Simplifying t = 23Solution
t = {3, 23}
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