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Simplifying 105 = 22t + -1t2 Solving 105 = 22t + -1t2 Solving for variable 't'. Reorder the terms: 105 + -22t + t2 = 22t + -22t + -1t2 + t2 Combine like terms: 22t + -22t = 0 105 + -22t + t2 = 0 + -1t2 + t2 105 + -22t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 105 + -22t + t2 = 0 Factor a trinomial. (7 + -1t)(15 + -1t) = 0Subproblem 1
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15Solution
t = {7, 15}
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