Rewrite 2x^2 + 2y^2 -8x +10y + 2 = 0 in standard form. find the center and radius of the circle. show all of your work for full credit.

In form
(x-h)^2+(y-k)^2=r^2
center is (h,k) and radius is r

complete the squaer for everybody
group x and y's sepereatley

(2x^2-8x)+(2y^2+10y)+2=0
undistribute  the quadratic coefneints
2(x^2-4x)+2(y^2+5y)+2=0
take 1/2 of each linear coefient, squaer them then add negtive and positive inside psarenthaseses
-4/2=-2, (-2)^2=4
5/2=2.5, 2.5^2=6.25

2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0
factor perfect squares
2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0
expand
2(x-2)^2-8+2(y+2.5)^2-12.5+2=0
2(x-2)^2+2(y+2.5)^2-18.5=0
add 18.5 to both sides
2(x-2)^2+2(y+2.5)^2=18.5
divide both sides by 2
(x-2)^2+(y+2.5)^2=9.25
(x-2)^2+(y-(-2.5))^2=(√9.25)^2
the center is (2,-2.5) and radius is √9.25