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