I know that this results in a cartesian equation for a circl

I know that this results in a cartesian equation for a circle, but I am having trouble getting the final equation right. Please go through, step-by-step so I can see where I am going wrong. Thank you.

Solution

r = 8 sin theta + 8 cos theta

r * r = r * (8 sin theta + 8 cos theta)

r^2 = 8r sin theta + 8r cos theta

x = r cos theta

y = r sin theta

x^2 + y^2 = r^2

r^2 = 8(r sin theta) + 8(r cos theta)

x^2 + y^2 = 8y + 8x

x^2 - 8x + y^2 - 8y = 0

Complete the squares.

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

(x - 4)^2 + (y - 4)^2 = 32

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