Question 1011480
{{{ x^2 + 2x + 6 = 0 }}}
You can complete the square
{{{ x^2 + 2x = -6 }}}
{{{ x^2 + 2x + (2/2)^2 = -6 + (2/2)^2 }}}
{{{ x^2 + 2x + 1 = -6 + 1 }}}
{{{ ( x + 1 )^2 = -5 }}}
Take the square root of both sides
{{{ x + 1 = + sqrt(5)*i }}}
{{{ x = -1 + sqrt(5)*i }}}
and, also
{{{ x = -1 - sqrt(5)*i }}}
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I will check one of these answers and
you can check the other one
{{{ x^2 + 2x + 6 = 0 }}}
{{{ ( -1 + sqrt(5)*i )^2 + 2*( -1 + sqrt(5)*i ) + 6 = 0 }}}
{{{ 1 - 2*sqrt(5)*i - 5 - 2 + 2*sqrt(5)*i + 6 = 0 }}}
{{{ 1 - 5 - 2 + 6  - 2*sqrt(5)*i + 2*sqrt(5)*i = 0 }}}
{{{ 0 = 0 }}}
OK