X² + 2x + y2 - 6y =-6

Correct  (x + 1)² + (y - 3)² = 4

Step-by-step explanation:

Given:

x² + 2 x + y² - 6 y = - 6

I suppose your question should have been to:

Write the standard form of the circle equation

First, we will form a complete square of the binomial for both variables.

x² + 2 x + 1² - 1² + y² - 2 y 3 + 3² - 3² = - 6

(x + 1)² + (y - 3)² - 1 - 9 = - 6

(x + 1)² + (y - 3)² = 10 - 6

(x + 1)² + (y - 3)² = 4

This is the standard form of the circle equation

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