Verified answer

X2+16⁢x+88+y2+14⁢y=0

Answer is:

(x + 8)^2 - 8^2 + (y + 7)^2 - 7^2 = - 88

(x + 8)^2 + (y + 7)^2 = - 88 + 64 + 49

(x + 8)^2 + (y + 7)^2 = 5^2

so the centre is (-8, -7) and the radius is 5

OR you can use

x^2 + y^2 + 2gx + 2fy + c = 0

x^2 + y^2 + 16x + 14y + 88 =0

g = 8, h = 7 and c = 88

Centre is (-g , -f) and the radius is sqrt(g^2 + f^2 - c)

Centre is (-8 , -7) and the radius is sqrt(8^2 + 7^2 - 88) = 5

First rearrange the equation to put the 88 on the right side

x^2+16x+y^2+14y = -88

complete the squares on the left side

x^2+16x+64+y^2+14y+49 = -88+64+49

factor left side

(x+8)^2 + (y+7)^2 = 25

center of circle at (-8,-7) with a radius of root 25 or 5

x^2+16x+y^2+14y=-88

(x+8)^2+(y+7)^2=-88+64+49

(x+8)^2+(y+7)^2=25

therefore circle center (-8.-7) and radius of 5