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Simplifying T(x) = x(50 + -2x) Multiply T * x xT = x(50 + -2x) xT = (50 * x + -2x * x) xT = (50x + -2x2) Solving xT = 50x + -2x2 Solving for variable 'x'. Reorder the terms: -50x + xT + 2x2 = 50x + -2x2 + -50x + 2x2 Reorder the terms: -50x + xT + 2x2 = 50x + -50x + -2x2 + 2x2 Combine like terms: 50x + -50x = 0 -50x + xT + 2x2 = 0 + -2x2 + 2x2 -50x + xT + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -50x + xT + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-50 + T + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-50 + T + 2x)' equal to zero and attempt to solve: Simplifying -50 + T + 2x = 0 Solving -50 + T + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + T + 50 + 2x = 0 + 50 Reorder the terms: -50 + 50 + T + 2x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + T + 2x = 0 + 50 T + 2x = 0 + 50 Combine like terms: 0 + 50 = 50 T + 2x = 50 Add '-1T' to each side of the equation. T + -1T + 2x = 50 + -1T Combine like terms: T + -1T = 0 0 + 2x = 50 + -1T 2x = 50 + -1T Divide each side by '2'. x = 25 + -0.5T Simplifying x = 25 + -0.5TSolution
x = {0, 25 + -0.5T}
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