COMPLEX NUMBER PROBLEM
x2+(2x+6)2=(2x+4)2,
x2=(2x+4)2-(2x+6)2,
x2=(2x+4+2x+6)(2x+4-2x-6)=(4x+10)(-2),
x2+2(4x+10)=0,
x2+8x+20=0,
x2+8x=-20,
x2+8x+16=16-20=-4,
(x+4)2=-4=-22,
x+4=±2i where i=√-1 (imaginary),
x=-4±2i (complex number), so x=-4+2i or -4-2i.
CHECK
x2+(2x+6)2=
(-4±2i)2+(-8±4i+6)2=
16∓16i-4+(-2±4i)2=
16∓16i-4+4∓16i-16=
∓32i;
(2x+4)2=
(2(-4±2i)+4)2=
(-8±4i+4)2=
(-4±4i)2=16(-1±i)2=16(1∓2i-1)=∓32i.
Therefore x2+(2x+6)2=(2x+4)2, when x=-4±2i.