Quadratics, change to turning point form: kx^2 + 2x + k = 0?

Question

Ok, here's what I did:
x^2 + 2x/k + k/k

x^2 + 2x/k + 1 + k/k - 1

What next? Or am I doing it wrong?

Please answer with explanations!

Thanks a lot

Answer 1

x² + (2/k).x + 1 = 0
(x² + (2/k).x + 1 / k²) - 1 / k² + 1 = 0
( x + (1 / k) )² = (1 / k²) - 1
(x + (1/k) )² = (1 - k).(1 + k) / k²
(x + (1/k)) = ±√((1 - k).(1 + k)) / k
x = - (1/k) ±√((1 - k).(1 + k)) / k