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# help algebra

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Let x and y be real numbers such that x^2 + y^2 = 2x + 4y + 2x + 8y.  Find the largest possible value of x.

Apr 19, 2022

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The largest possible value of x is the x-coordinate of the center + radius

We find both as follows:

Simplify: $$x^2+y^2-12y-4x=0$$

Completing the square, we have: $$(x-2)^2+(y-6)^2=40$$

The x-co-ordinate is 2, and the radius is $$\sqrt{40}$$

Thus, the answer is $$\color{brown}\boxed{2+2\sqrt{10}}$$

Apr 19, 2022