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Solve  $x^{2}-2 x-2=0$  by completing the square
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Step 1 . Move the constant term to the right:
$$x^{2}-2 x=2$$

Step 2. Add the square of half the coefficient of $x$ to both sides. In this case, add the square of half of $-2$ i.e. add the square of $-1$.

$$x^{2}-2 x+1=2+1$$
The left-hand side is now the perfect square of $(x-1)$
$$(x-1)^{2}=3$$
We know that if $a^{2}=b, a=\pm \sqrt{b}$
Therefore, $x-1=\pm \sqrt{3}$
$$x=1 \pm \sqrt{3}$$

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