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Simplifying 40(t) = -1t2 + 14t Reorder the terms: 40t = 14t + -1t2 Solving 40t = 14t + -1t2 Solving for variable 't'. Combine like terms: 40t + -14t = 26t 26t + t2 = 14t + -1t2 + -14t + t2 Reorder the terms: 26t + t2 = 14t + -14t + -1t2 + t2 Combine like terms: 14t + -14t = 0 26t + t2 = 0 + -1t2 + t2 26t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 26t + t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(26 + t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(26 + t)' equal to zero and attempt to solve: Simplifying 26 + t = 0 Solving 26 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + t = 0 + -26 Combine like terms: 26 + -26 = 0 0 + t = 0 + -26 t = 0 + -26 Combine like terms: 0 + -26 = -26 t = -26 Simplifying t = -26Solution
t = {0, -26}
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