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Simplifying A(x) = -1x2 + 90x Multiply A * x xA = -1x2 + 90x Reorder the terms: xA = 90x + -1x2 Solving xA = 90x + -1x2 Solving for variable 'x'. Reorder the terms: -90x + xA + x2 = 90x + -1x2 + -90x + x2 Reorder the terms: -90x + xA + x2 = 90x + -90x + -1x2 + x2 Combine like terms: 90x + -90x = 0 -90x + xA + x2 = 0 + -1x2 + x2 -90x + xA + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -90x + xA + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-90 + 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 '(-90 + A + x)' equal to zero and attempt to solve: Simplifying -90 + A + x = 0 Solving -90 + A + x = 0 Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + A + 90 + x = 0 + 90 Reorder the terms: -90 + 90 + A + x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + A + x = 0 + 90 A + x = 0 + 90 Combine like terms: 0 + 90 = 90 A + x = 90 Add '-1A' to each side of the equation. A + -1A + x = 90 + -1A Combine like terms: A + -1A = 0 0 + x = 90 + -1A x = 90 + -1A Simplifying x = 90 + -1ASolution
x = {0, 90 + -1A}
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