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Simplifying 80t + -5t2 = 275 Solving 80t + -5t2 = 275 Solving for variable 't'. Reorder the terms: -275 + 80t + -5t2 = 275 + -275 Combine like terms: 275 + -275 = 0 -275 + 80t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-55 + 16t + -1t2) = 0 Factor a trinomial. 5((-11 + t)(5 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-11 + t)' equal to zero and attempt to solve: Simplifying -11 + t = 0 Solving -11 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + t = 0 + 11 t = 0 + 11 Combine like terms: 0 + 11 = 11 t = 11 Simplifying t = 11Subproblem 2
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 = 5Solution
t = {11, 5}
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