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x^{2}+8x+1=x^{2}
Anything plus zero gives itself.
x^{2}+8x+1-x^{2}=0
Subtract x^{2} from both sides.
8x+1=0
Combine x^{2} and -x^{2} to get 0.
8x=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-1}{8}
Divide both sides by 8.
x=-\frac{1}{8}
Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.