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4+64-16x+x^{2}=x^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-x\right)^{2}.
68-16x+x^{2}=x^{2}
Add 4 and 64 to get 68.
68-16x+x^{2}-x^{2}=0
Subtract x^{2} from both sides.
68-16x=0
Combine x^{2} and -x^{2} to get 0.
-16x=-68
Subtract 68 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-68}{-16}
Divide both sides by -16.
x=\frac{17}{4}
Reduce the fraction \frac{-68}{-16} to lowest terms by extracting and canceling out -4.