# Complete the square to write the equation x^2 + y^2 – 4x – 16 = 0 in graphing form.

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Expert Answers

hala718 | Certified Educator

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For the equation x^2 + y^2 - 4x -16 = 0

We need to solve by completing the square.

==> First we will group terms.

==> x^2 - 4x + y^2 - 16 = 0

==> (x^2 -4x) + y^2 -16= 0

==> (x^2 -4x +4 -4) + y^2 -16= 0

==> (x-2)^2 -4 + y^2 = 16

==> (x-2)^2 + y^2 = 20

**Then we have equation of a circle such that:**

**(2, 0) is the center of the circle and sqrt20 is the radius.**

justaguide | Certified Educator

The equation x^2 + y^2 - 4x - 16 = 0 can be rewritten as follows:

x^2 + y^2 - 4x - 16 = 0

completing the squares

=> x^2 - 4x + 4 + y^2 = 16 + 4

=> (x - 2)^2 + y^2 = 20

=> (x - 2)^2 + ( y - 0)^2 = (sqrt 20)^2

This is the equation of a circle with center (2, 0) and radius sqrt 20.

**The required equation is (x - 2)^2 + ( y - 0)^2 = (sqrt 20)^2**