Solution 2.3:1a
From Förberedande kurs i matematik 1
If we consider the squaring rule
\displaystyle \left( x-a \right)^{2}=x^{2}-2ax+a^{2}
and move \displaystyle a^{2} over to the left-hand side, we obtain the formula
\displaystyle \left( x-a \right)^{2}-a^{2}=x^{2}-2ax
\displaystyle
With the help of this formula, we can rewrite (complete the square of) a mixed expression
\displaystyle x^{2}-2ax
to a obtain a quadratic expression,
\displaystyle \left( x-a \right)^{2}-a^{2}
.
The expression \displaystyle x^{2}-2x corresponds to \displaystyle a=1 in the formula above and thus
\displaystyle x^{2}-2x=\left( x-1 \right)^{2}-1
