Question 58198
Solve by completing the square:
{{{x^2 + 2 = 2x}}} Subtact 2x from both sides.
{{{x^2 - 2x + 2 = 0}}} Subtract 2 from both sides.
{{{x^2 - 2x = -2}}} Add the square of half the x-coefficient ((-2/2)^2 = 1) to both sides.
{{{x^2 - 2x + 1 = -1}}} Factor the left side.
{{{(x-1)^2 = -1}}} Take the square root of both sides.
{{{x-1 }}}= +/-{{{sqrt(-1)}}} Add 1 to both sides.
{{{x = 1+sqrt(-1)}}} and {{{x = 1-sqrt(-1)}}} which you can write as:
{{{x = 1+i}}} and {{{x = 1-i}}} Where: {{{i = sqrt(-1)}}}