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Simplifying A(x) = x(250 + -1x) Multiply A * x xA = x(250 + -1x) xA = (250 * x + -1x * x) xA = (250x + -1x2) Solving xA = 250x + -1x2 Solving for variable 'x'. Reorder the terms: -250x + xA + x2 = 250x + -1x2 + -250x + x2 Reorder the terms: -250x + xA + x2 = 250x + -250x + -1x2 + x2 Combine like terms: 250x + -250x = 0 -250x + xA + x2 = 0 + -1x2 + x2 -250x + xA + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -250x + xA + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-250 + A + x) = 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 '(-250 + A + x)' equal to zero and attempt to solve: Simplifying -250 + A + x = 0 Solving -250 + A + x = 0 Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + A + 250 + x = 0 + 250 Reorder the terms: -250 + 250 + A + x = 0 + 250 Combine like terms: -250 + 250 = 0 0 + A + x = 0 + 250 A + x = 0 + 250 Combine like terms: 0 + 250 = 250 A + x = 250 Add '-1A' to each side of the equation. A + -1A + x = 250 + -1A Combine like terms: A + -1A = 0 0 + x = 250 + -1A x = 250 + -1A Simplifying x = 250 + -1ASolution
x = {0, 250 + -1A}
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