Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20

Center of the circle → (-1, -2)

Radius of the circle = 5 units

Step-by-step explanation:

Given equation for a circle is,

x² + 2x + y² + 4y = 20

By completing the square we will rewrite this equation as,

(x² + 2x + 1 - 1) + [y² + 2(2)y + 4 - 4] = 20

(x² + 2x + 1) - 1 + [y² + 2(2y) + 4] - 4 = 20

(x + 1)² - 1 + (y + 2)² - 4 = 20

(x + 1)² + (y + 2)² - 5 = 20

(x + 1)² + (y + 2)² = 5²  (1)

Since standard equation of a circle is represented by,

(x - h)² + (y - k)² = r²

where (h, k) is the center and 'r' is the radius of the circle

By comparing the standard equation of a circle with the given equation (1),

(-1, -2) will be the center and radius of the circle will be 5 units.

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step-by-step explanation: