Question

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 + )2 + (y + )2 =

Answer 1

Let's first write each step of the procedure:
 Step 1: 
 group the x terms together and the terms and together, and move the constant term to the other side of the equation:
 x² + 12x + y² + 2y = 1
 Step 2:
 determine (b ÷ 2) 2 for the x and y terms.
 (12 ÷ 2) 2 = 36
 and
 (2 ÷ 2) 2 = 1
 Step 3:
 add the values to both sides of the equation.
 x2 + 12x + 36 + y2 + 2y + 1 = 1 + 36 + 1
 Step 4:
 write each trinomial to binomial squared, and simplify the right side.
 (x + 6) 2 + (y + 1) 2 = 38
 Answer:
 the last step is:
 (x + 6) 2 + (y + 1) 2 = 38