Question 944912
Imaginary numbers allow ways to deal with {{{ sqrt(-1) }}}
{{{ x^2 - 4x + 8  = 0 }}}
Complete the square
{{{ x^2  - 4x = -8 }}}
Take {{{ 1/2 }}} of the coefficient of 
{{{ x }}}, square it, and add it to both sides
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{{{ x^2  - 4x + ( -4/2 )^2 = -8 + ( -4/2 )^2 }}}
{{{ x^2 - 4x + 4 = -8 + 4 }}}
{{{ x^2  - 4x + 4 = -4 }}}
{{{ ( x - 2 )^2 = -4 }}}
Take the square root of both sides
{{{ x - 2 = sqrt( -4 ) }}}
{{{ x - 2 = sqrt( -1*4 ) }}}
{{{ x - 2 = sqrt( -1 ) * sqrt( 4 ) }}}
{{{ x - 2 = 2i }}}
{{{ x = 2 + 2i }}}
and also, 
{{{ x - 2 = -2i }}}
{{{ x = 2 - 2i }}}
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The factors of the equation are:
{{{ ( x - 2 - 2i )*( x - 2 + 2i ) = x^2 - 4x + 8 }}}
You can prove this just by multiplying it out