we are given
[tex] 2x^2+2y^2-28x+20y+20=0 [/tex]
we can see that
each terms are multiple of 2
so, we can factor out 2
[tex] 2(x^2+y^2-14x+10y+10)=0 [/tex]
we can divide both sides by 2
[tex] x^2+y^2-14x+10y+10=0 [/tex]
we can rearrange it
[tex] x^2+-14x+y^2+10y+10=0 [/tex]
now, we can move 10 on right side
[tex] x^2+-14x+y^2+10y=-10 [/tex]
[tex] x^2+-2*7*x+y^2+2*5*y=-10 [/tex]
now, we can add both sides 7^2 and 5^2
[tex] x^2+-2*7*x+7^2+y^2+2*5*y+5^2=-10+7^2+5^2 [/tex]
[tex] (x-7)^2+(y+5)^2=-10+7^2+5^2 [/tex]
we can simplify it
[tex] (x-7)^2+(y+5)^2=64 [/tex]
we can also write as
[tex] (x-7)^2+(y+5)^2=8^2 [/tex]..............Answer
