Question 1056414
{{{ x^2 + 4x + 8 = 0 }}}
I can complete the square to solve
{{{ x^2 + 4x = -8 }}}
{{{ x^2 + 4x + (4/2)^2 = -8 + (4/2)^2 }}}
{{{ x^2 + 4x + 4 = -8 + 4 }}}
{{{ ( x + 2 )^2 = -4 }}}
Take the square root of both sides
{{{ x + 2 = sqrt(-4) }}}
{{{ x + 2 = 2i }}}
{{{ x = -2 + 2i }}}
and, also, taking the negative square root of {{{ -4 }}},
{{{ x + 2 = -sqrt(-4) }}}
{{{ x + 2 = -2i }}}
{{{ x = -2 - 2i }}}
-----------------------
The roots are {{{ -2 + 2i }}} and {{{ -2 - 2i }}}
---------------------------------------------
To check, you can plug either solution for {{{ x }}}
back into original equation, like this:
{{{ x^2 + 4x + 8 = 0 }}}
{{{ ( -2 + 2i )^2 + 4*( -2 + 2i ) + 8 = 0 }}}
You can do the checks