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Simplifying A(x) = 2x2 + 40x Multiply A * x xA = 2x2 + 40x Reorder the terms: xA = 40x + 2x2 Solving xA = 40x + 2x2 Solving for variable 'x'. Reorder the terms: -40x + xA + -2x2 = 40x + 2x2 + -40x + -2x2 Reorder the terms: -40x + xA + -2x2 = 40x + -40x + 2x2 + -2x2 Combine like terms: 40x + -40x = 0 -40x + xA + -2x2 = 0 + 2x2 + -2x2 -40x + xA + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -40x + xA + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + 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 '(-40 + A + -2x)' equal to zero and attempt to solve: Simplifying -40 + A + -2x = 0 Solving -40 + A + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + A + 40 + -2x = 0 + 40 Reorder the terms: -40 + 40 + A + -2x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + A + -2x = 0 + 40 A + -2x = 0 + 40 Combine like terms: 0 + 40 = 40 A + -2x = 40 Add '-1A' to each side of the equation. A + -1A + -2x = 40 + -1A Combine like terms: A + -1A = 0 0 + -2x = 40 + -1A -2x = 40 + -1A Divide each side by '-2'. x = -20 + 0.5A Simplifying x = -20 + 0.5ASolution
x = {0, -20 + 0.5A}
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