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Simplifying A(x) = 80x + -2x2 Multiply A * x xA = 80x + -2x2 Solving xA = 80x + -2x2 Solving for variable 'x'. Reorder the terms: -80x + xA + 2x2 = 80x + -2x2 + -80x + 2x2 Reorder the terms: -80x + xA + 2x2 = 80x + -80x + -2x2 + 2x2 Combine like terms: 80x + -80x = 0 -80x + xA + 2x2 = 0 + -2x2 + 2x2 -80x + xA + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -80x + xA + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-80 + A + 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 '(-80 + A + 2x)' equal to zero and attempt to solve: Simplifying -80 + A + 2x = 0 Solving -80 + A + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + A + 80 + 2x = 0 + 80 Reorder the terms: -80 + 80 + A + 2x = 0 + 80 Combine like terms: -80 + 80 = 0 0 + A + 2x = 0 + 80 A + 2x = 0 + 80 Combine like terms: 0 + 80 = 80 A + 2x = 80 Add '-1A' to each side of the equation. A + -1A + 2x = 80 + -1A Combine like terms: A + -1A = 0 0 + 2x = 80 + -1A 2x = 80 + -1A Divide each side by '2'. x = 40 + -0.5A Simplifying x = 40 + -0.5ASolution
x = {0, 40 + -0.5A}
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