Answer:
(x + 2)² + y² = 4
Explanation:
If we have an equation with the form:
x² + bx = c
We can complete the square by adding (b/2)² to both sides.
In this case, we have:
x² + y² + 4x = 0
So, we can organize the terms as:
(x² + 4x) + y² = 0
Therefore, to complete the square of (x² + 4x) we need to add:
[tex](\frac{b}{2})^2=(\frac{4}{2})^2=2^2=4[/tex]
Then:
(x² + 4x + 4) + y² = 0 + 4
(x + 2)² + y² = 4
On the other hand, the equation of a circumference is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center and r is the radius.
So, we can rewrite the equation as:
(x + 2)² + y² = 4
(x -(-2)² + (y - 0)² = 2²
Therefore, the center is the point (-2, 0) and the radius is 2. So, the graph of the circle is:
