Answer:
(x + 6)² + (y + 1)² = 36 + 1 + 1
Step-by-step explanation:
using the steps given, we are left with:
x² + 12x + 36 + y² + 2x + 1 = 38
we can factor each term in parentheses:
(x² + 12x + 36) + (y² + 2x + 1) = 36 + 1 + 1
lets start with x² + 12x + 36. we factor by finding 2 numbers that add up to 12 and when multiplied together get 36. the answer is 6. so we can factor:
(x + 6)²
next we factor y² + 2x + 1. the same rules apply, and this number would be 1.
(y + 1)²
we have the following:
(x + 6)² + (y + 1)² = 36 + 1 + 1
to simplify the right side, we add the terms, then square it as well to find the radius of the circle, in which the formula is (x - h)² + (y - k)² = r²
(x + 6)² + (y + 1)² = 38²
(x + 6)² + (y + 1)² = 1444
(x + 6)² + (y + 1)² = √1444
(x + 6)² + (y + 1)² = 38
this is the final form
