Persamaan kuadrat x2+4x+k=0, x1 dan x2, jika x1 kuadrat-x2 kuadrat=-32 Berapa kah nilai k ?

x²+4x+k=0
x1+x2=-b/a=-4/1=-4
x1x2=c/a=k

x1²-x2²=-32
(x1-x2)(x1+x2) = -32
(x1-x2)(-4)=-32
x1-x2= -32/-4
x1-x2=8
(x1-x2)²=8²
x1²-2(x1+x2)+x2²=64
(x1+x2)²-2x1x2-2(x1+x2)=64
(-4)²-2(k) -2(-4)=64
16-2k+8=64
-2k+24=84
-2k=84-24
-2k=60
k=60/-2
k=-30