Question 164562
This may not be the best example to learn from.
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{{{n(x)=(x^2+2)/2=0}}}.....Set the equation equal to zero.
{{{x^2+2=0}}}.....Multiply both sides by 2.
{{{x^2=-2}}}.....Subtract 2 from boths sides. 
{{{x=0 +- sqrt(-2)}}}.....Take the square root of both sides.
{{{x=0 +- sqrt(2)*sqrt(-1)}}}.....Factor out the square root of 2.
{{{x=0 +- sqrt(2)i}}}.....Replace square root of -1 with complex i.
where
{{{i=sqrt(-1)}}}
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This equation has no real roots only complex (complex conjugates) roots.