#x^2+25# is in the form #ax^2+bx+c#, with #a=1#, #b=0# and #c=25#.
This has discriminant #Delta# given by the formula:
#Delta = b^2-4ac = 0^2 - (4xx1xx25) = -100 = -10^2#
Since #Delta < 0# the equation #x^2+25 = 0# has no real roots. It has a pair of distinct complex conjugate roots, namely #+-5i#
The discriminant #Delta# is the part under the square root in the quadratic formula for roots of #ax^2+bx+c = 0# ...
#x = (-b +-sqrt(b^2-4ac))/(2a) = (-b +-sqrt(Delta))/(2a)#
So if #Delta > 0# the equation has two distinct real roots.
If #Delta = 0# the equation has one repeated real root.
If #Delta < 0# the equation has no real roots, but two distinct complex roots.
In our case the formula gives:
#x = (-0 +-10i)/2 = +-5i#
