How do you solve the equation $x^2-4x+5=0$ by completing the square?

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Answer 1 · 2017-03-06T16:07:21

$x=2+-i$

$x^2-4x+5=0$

1) half the coefficient of $x$ square, add and subtract to balance

$color(blue)(x^2-4x+2^2)+5-2^2=0$

$"2) the blue terms form a perfect square"$

$color(blue)((x-2)^2)+5-4=0$

$(x-2)^2+1=0$

3) solve for $x$

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

$x-2=+-sqrt(-1)$

$x-2=+-i$

$:.x=2+-i$

How do you solve the equation x^2-4x+5=0x^2-4x+5=0 by completing the square?