...find the values of k for which the line y= x+2 meets the curve y² + (x+k)²=2

i sub (x+2)² into y²

the i got 2x² + 4x +2 -2k +k² = 0<<<<<< this line should read 2x² + 4x +2+2kx+k² = 0

then b² -4ac is more than or equal zero.

i got 4² -(4)(2)(2-2k+k²)

--> 8k² +16

but my ans was not correct. the range of k is 0 to 4.i didnt get that