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Simplifying F(x) = x2 + -12x Multiply F * x xF = x2 + -12x Reorder the terms: xF = -12x + x2 Solving xF = -12x + x2 Solving for variable 'x'. Reorder the terms: 12x + xF + -1x2 = -12x + x2 + 12x + -1x2 Reorder the terms: 12x + xF + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 12x + xF + -1x2 = 0 + x2 + -1x2 12x + xF + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12x + xF + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + F + -1x) = 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 '(12 + F + -1x)' equal to zero and attempt to solve: Simplifying 12 + F + -1x = 0 Solving 12 + F + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + F + -12 + -1x = 0 + -12 Reorder the terms: 12 + -12 + F + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + F + -1x = 0 + -12 F + -1x = 0 + -12 Combine like terms: 0 + -12 = -12 F + -1x = -12 Add '-1F' to each side of the equation. F + -1F + -1x = -12 + -1F Combine like terms: F + -1F = 0 0 + -1x = -12 + -1F -1x = -12 + -1F Divide each side by '-1'. x = 12 + F Simplifying x = 12 + FSolution
x = {0, 12 + F}
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