616. 
Factor 8 from the two y terms.
x 2 + 8(y 2 – 4y) = 0
Complete the square within the parentheses by adding 4. You have to add 8(4) to the right side, because the numbers in the parentheses are being multiplied, too.
x 2 + 8(y 2 – 4y + 4) = 8(4)
Write the trinomial in the parentheses as the square of a binomial, and simplify on the right.
x 2 + 8(y – 2)2 = 32
Now divide each term in the equation by 32 and reduce the fractions.
617. 
Group the x terms and y terms together; add 9 to each side of the equation.
2x 2 – 4x + y 2 + 6y = 9
Factor 2 from the two x terms.
2(x 2 – 2x) + y 2 + 6y = 9
Complete the square within the parentheses by adding 1. You have to add 2(1) to the right side, because the number in the parentheses is being multiplied, too. Also, complete the square involving the y terms by adding 9; add 9 to the right side, too.
2(x 2 – 2x + 1) + (y 2 + 6y + 9) = 9 + 2 + 9
Write the trinomials as the squares of binomials, and simplify on the right.
2(x – 1)2 + (y + 3)2 = 20
Now divide each term in the equation by 20 and reduce the fractions.
618.
