Answer:
Some relationships:
Angle FGH + Angle FHG = 90
sin(FGH) = cos(FHG)
cos(FGH) = sin(FHG)
Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c
Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4
-4 < 0, therefor there are no roots
(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)
7.07 is the right answer to 7.07106781187 rounded to the nearest hundredth
