Finding the roots by completing the square

For y=x^2-6x-11

complete the square

so roots

set y=0

0=x^2-6x-11

group x terms

0 = (x^2-6x) - 11

take 1/2 of linear coefient (-6) and square it

-6/2=-3, (-3) ^2=9

add positive and neative to inside of parenthasees

0 = (x^2-6x+9-9) - 11

complete square

0 = ((x-3) ^2-9) - 11

expand

0 = (x-3) ^2-9-11

0 = (x-3) ^2-20

add 20 to both sides

20 = (x-3) ^2

sqrt both sides

remember positive and negative roots

+/-2√5=x-3

add 3 to both sides

3+/-2√5=x

so

x=3+2√5 and 3-2√5