Put the x terms together and the y terms together and subtract the constant
term from both sides:
Factor the 4 out of the first three terms and factor 2 out of the last
three terms on the left, skipping a space at the end of each parentheses:
Complete the square in the first parentheses:
To the side or in your head,
1. Multiply the coefficient of x, which is 8, by 1/2, getting 4
2. Square 4, getting 16.
3. Add inside the first parentheses
4. Add 4 times 16 or +64 to the right side, since the first parentheses
is multiplied by 4.
Complete the square in the second parentheses:
To the side or in your head,
1. Multiply the coefficient of y, which is 2, by 1/2, getting 1
2. Square 1, getting 1.
3. Add 1 inside the second parentheses
4. Add 2 times 1 or +2 to the right side, since the second parentheses
is multiplied by 2.
Factor the trinomials inside the parentheses, combine the numbers on
the right:
Write the two equal factors as squares of binomials:
Get 1 on the right side by dividing every term by 64
Divide each numerator and denominator on the left by the coefficient
of the squared binomial in the numerator:
Edwin
