x2+x++2k (x2-x-1) = 0 is a perfect square for hw many values of k? pls answer

The given quadratic polynomial is x2+x+2kx2-x-1 = 0
x2+x+2kx2-2kx-2k = 0x21+2k+1-2kx-2k = 0
To be a perfect square the value Discriminant; D = 0 so we have;
D = 01-2k2-41+2k-2k = 01+4k2-4k+8k1+2k = 01+4k2-4k+8k+16k2 = 020k2+4k+1 = 0k = -4±42-4×20×12×20k = -4±-6440k = -4±8×8×-140k = -4±8-140k = -4±8i40k = -4+8i40 and k = -4-8i40k = -1+2i10 and k = -1-2i10

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