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x^{2}-4x+4-x^{2}=1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
-4x+4=1
Combine x^{2} and -x^{2} to get 0.
-4x=1-4
Subtract 4 from both sides.
-4x=-3
Subtract 4 from 1 to get -3.
x=\frac{-3}{-4}
Divide both sides by -4.
x=\frac{3}{4}
Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.