Step 1: Divide each term by 2
x2+6x+y2−8y−75=0
BLANK 1: add 75 to both sides
x2+6x+y2−8y−75+75=+75
x2+6x+y2−8y=75
BLANK 2: add 9 to both sides to complete the squares for the x's
x2+6x+9+y2−8y=84
BLANK 3: add 16 to both sides to complete the squares for the y's
x2+6x+9+y2−8y+16=100
Step 5: Rewrite x's as a perfect square
[tex]x^{2}+6x+9= (x+3)^{2}[/tex]
Step 6: Rewrite y's as a perfect square
[tex]y^{2}-8y-16=(y-4)^{2}[/tex]
Step 7:
Standard form of the equation: [tex](x+3)^{2}+(y-4)^{2}=100[/tex]