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Simplifying 200 = 250 + -5T + -1T2 Solving 200 = 250 + -5T + -1T2 Solving for variable 'T'. Combine like terms: 200 + -250 = -50 -50 + 5T + T2 = 250 + -5T + -1T2 + -250 + 5T + T2 Reorder the terms: -50 + 5T + T2 = 250 + -250 + -5T + 5T + -1T2 + T2 Combine like terms: 250 + -250 = 0 -50 + 5T + T2 = 0 + -5T + 5T + -1T2 + T2 -50 + 5T + T2 = -5T + 5T + -1T2 + T2 Combine like terms: -5T + 5T = 0 -50 + 5T + T2 = 0 + -1T2 + T2 -50 + 5T + T2 = -1T2 + T2 Combine like terms: -1T2 + T2 = 0 -50 + 5T + T2 = 0 Factor a trinomial. (-10 + -1T)(5 + -1T) = 0Subproblem 1
Set the factor '(-10 + -1T)' equal to zero and attempt to solve: Simplifying -10 + -1T = 0 Solving -10 + -1T = 0 Move all terms containing T to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1T = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1T = 0 + 10 -1T = 0 + 10 Combine like terms: 0 + 10 = 10 -1T = 10 Divide each side by '-1'. T = -10 Simplifying T = -10Subproblem 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 = {-10, 5}
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