Y^2-5y+4=0

y^2-5y=-4

adding (5/2)^2 on both sises to complete the square

y^2-5y+(5/2)^2=-4+(5/2)^2

(y-5/2)^2=-4+25/4

(y-5/2)^2=-16+25 /4

(y-5/2)^2=9/4

squaring on both sides

(y-5/2)=+3/2

y=5/2+3/2

y=5/2+3/2; y=5/2-3/2

y=4 ; y=1

y^2-5y=-4

adding (5/2)^2 on both sises to complete the square

y^2-5y+(5/2)^2=-4+(5/2)^2

(y-5/2)^2=-4+25/4

(y-5/2)^2=-16+25 /4

(y-5/2)^2=9/4

squaring on both sides

(y-5/2)=+3/2

y=5/2+3/2

y=5/2+3/2; y=5/2-3/2

y=4 ; y=1