Question

there are four steps for converting the equation $x^{2}+y^{2}+12x+2y-1=0$ into standard form by completing the square. complete the last step.

1. group the x terms together and the y terms together, and move the constant term to the other side of the equation.

$x^{2}+12x+y^{2}+2y=1$

1. determine $(b \div 2)^{2}$ for the x and y terms.

$(12 \div 2)^{2}=36$ and $(2 \div 2)^{2}=1$

1. add the values to both sides of the equation.

$x^{2}+12x+36+y^{2}+2y+1=1+36+1$

1. write each trinomial as a binomial squared, and simplify the right side.

$(x+\square)^{2}+(y+\square)^{2}=\square$

Explanation:

Step1: Factor x-trinomial

$x^2 + 12x + 36 = (x+6)^2$

Step2: Factor y-trinomial

$y^2 + 2y + 1 = (y+1)^2$

Step3: Simplify right-hand side

$1 + 36 + 1 = 38$

Answer:

$(x + 6)^2 + (y + 1)^2 = 38$