How do you solve $x^2-2x+2$ by completing the square?

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Answer 1 · 2015-06-12T02:51:57

$x=1+i$

$x=1-i$

Make a perfect square trinomial by completing the square. A perfect square trinomial has the form of $a^2+2ab+b^2=(a+b)^2$ or $a^2-2ab+b^2=(a-b)^2$ .

$x^2-2x+2=0$

Subtract $2$ from both sides of the equation.

$x^2-2x=-2$

Divide the coefficient of the $x$ term by $2$ and square the result. Add it to both sides of the equation.

$(-2)/2=-1$ ; $-1^2=1$

$x^2-2x+1=-2+1$ =

$x^2-2x+1=-1$

There is now a perfect square trinomial on the left side of the equation.

Factor the trinomial.

$(x-1)^2=-1$

Take the square root of both sides and solve for $x$ .

$x-1=+-sqrt(-1)$

$x-1=+-i$

$x=1+-i$

How do you solve x^2-2x+2 x^2-2x+2 by completing the square?