#y^2 = 64 - 4x^2#
#y =+- sqrt(64 - 4x^2)#
#4x^2 - 56x + 9(sqrt(64 - 4x^2))^2 + 160 = 0#
#4x^2 - 56x + 9(64 - 4x^2) + 160 = 0#
#4x^2 - 56x + 576 - 36x^2 + 160 = 0#
#0 = 32x^2 + 56x - 736#
#0 = 8(4x^2 + 7x - 92)#
#0 = 8(4x^2 - 16x + 23x - 92)#
#0 = 8(4x(x - 4) + 23(x - 4))#
#0 = 8(4x + 23)(x - 4)#
#x = -23/4 and 4#
Case 1:
#4(-23/4)^2 + y^2 - 64 = 0#
#4(529/16) + y^2 - 64 = 0#
#y^2 = 64 - 529/4#
#y = O/#
Case 2:
#4(4)^2+ y^2 - 64 = 0#
#4(16) + y^2 - 64 = 0#
#y^2 = 64 - 64#
#y^2 = 0#
#y = 0#
The only real solution is #x = 4#, #y = 0#.
Thus, the solution set is #{-4, 0}#.
Hopefully this helps!