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Simplifying t2 + -18t + 60 = 1500 Reorder the terms: 60 + -18t + t2 = 1500 Solving 60 + -18t + t2 = 1500 Solving for variable 't'. Reorder the terms: 60 + -1500 + -18t + t2 = 1500 + -1500 Combine like terms: 60 + -1500 = -1440 -1440 + -18t + t2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1440 + -18t + t2 = 0 Factor a trinomial. (-30 + -1t)(48 + -1t) = 0Subproblem 1
Set the factor '(-30 + -1t)' equal to zero and attempt to solve: Simplifying -30 + -1t = 0 Solving -30 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1t = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1t = 0 + 30 -1t = 0 + 30 Combine like terms: 0 + 30 = 30 -1t = 30 Divide each side by '-1'. t = -30 Simplifying t = -30Subproblem 2
Set the factor '(48 + -1t)' equal to zero and attempt to solve: Simplifying 48 + -1t = 0 Solving 48 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + -1t = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -1t = 0 + -48 -1t = 0 + -48 Combine like terms: 0 + -48 = -48 -1t = -48 Divide each side by '-1'. t = 48 Simplifying t = 48Solution
t = {-30, 48}
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