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x^{2}-\left(x^{2}-2x+1\right)=25
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x^{2}-x^{2}+2x-1=25
To find the opposite of x^{2}-2x+1, find the opposite of each term.
2x-1=25
Combine x^{2} and -x^{2} to get 0.
2x=25+1
Add 1 to both sides.
2x=26
Add 25 and 1 to get 26.
x=\frac{26}{2}
Divide both sides by 2.
x=13
Divide 26 by 2 to get 13.