y2+5.875y+1=0,
y2+5.875y=-1, now complete the square on LHS:
y2+5.875y+(5.875/2)2=(5.875/2)2-1=7.6289 approx. (Note that the constant (5.875/2)2 has to be added to both sides.)
(y+5.875/2)2=7.6289,
y+5.875/2=±2.762 approx.
y=-5.875/2±2.762, giving us y=-0.1755 any y=-5.6995 approx.
The quadratic formula gives the same result.