There are four steps for converting the equation x2 + y2 + 12x + 2y – 1 = 0 into standard form by completing the square. Complete the last step.
Group the x terms together and the y terms together, and move the constant term to the other side of the equation.
x²+ 12x + y²+ 2y = 1
Determine (b ÷ 2)2 for the x and y terms.
(12 ÷ 2)2 = 36 and (2 ÷ 2)2 = 1
Add the values to both sides of the equation.
x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1
Write each trinomial as a binomial squared, and simplify the right side.
(x +
12
)2 + (y +
37
)2 =
27
Group the x terms together and the y terms together, and move the constant term to the other side of the equation.
x²+ 12x + y²+ 2y = 1
Determine (b ÷ 2)2 for the x and y terms.
(12 ÷ 2)2 = 36 and (2 ÷ 2)2 = 1
Add the values to both sides of the equation.
x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1
Write each trinomial as a binomial squared, and simplify the right side.
(x +
12
)2 + (y +
37
)2 =
27