How do I factor this with the 2x^2 ?

Question

Find the center ( h,k ) and the radius of the circle 2x^2 + 10x +2y^2 + y - 8 = 0

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Answer 1 · 2016-10-28T15:34:52

centre is# (-5/2, -1/4)#

radius #r=sqrt(165/16)=sqrt165/4#

#2x^2+10x+2y^2+y-8=0#

to find centre of the circle we need to complete the squares on the x & y parts of the equation.

When completing the square get the coefficient of the square terms =1

Divide everything by 2 to begin with.

#x^2+5x+y^2+y/2-4=0#

#(x^2+5x)+(y^2+y/2)-4=0#

#(x^2+5x+(5/2)^2)+(y^2+y/2+(1/4)^2)-4-(5/2)^2-(1/4)^"=0#

#(x+5/2)^2+(y+1/4)^2-4-25/4-1/16=0#

#(x+5/2)^2+(y+1/4)^2=165/16#

cmp #(x-a)^2+(y-b)^2=r^2#

centre is# (-5/2, -1/4)#

radius #r=sqrt(165/16)=sqrt165/4#