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

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Answer 1 · 2016-04-27T17:15:46

The solutions are:
$color(green)(x = sqrt (-1) + 1$ or, $color(green)(x = -sqrt (-1) + 1$

$x^2 - 2x + 2$

$x^2 -2x = -2$

To write the Left Hand Side as a Perfect Square, we add 1 to both sides:

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

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

Using the Identity $color(blue)((a-b)^2 = a^2 - 2ab + b^2$ , we get

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

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

$color(green)(x = sqrt (-1) + 1$ or $color(green)(x = -sqrt (-1) + 1$

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