1. Square Roots

How do I find Cx

CD = sq. root{ [(sq. root (16 - (Cx-1)^2) + 2] - Cy }^2

Cx is supposed to equal + or - [sq. root (16- (CD+1)^2 ] +1

2. CD, Cx, Cy ... what do these mean?

3. CD is a length

Cx is the x coordinate of C
and Cy is the y coordinate of C

I just need help how to get Cx outta there....

4. CD = sq. root{ [(sq. root (16 - (Cx-1)^2) + 2] - Cy }^2
I can't interpret your syntax ... how did you determine this for segment CD?

It might help to know what the original problem statement says in its entirety.

5. Create a rule that allows you to predict the location of C when you know the length of CD,

Ignore the sentence to the right, that was a different problem involving the circle...

6. point D is on the circle. the coordinates for point D are

$(x, \sqrt{16-(x-1)^2} + 2)$

point C has coordinates $(x,3)$

CD is the vertical distance between D and C ... the difference between the y-values.

$CD = [\sqrt{16-(x-1)^2} + 2] - 3$

$CD = \sqrt{16-(x-1)^2} - 1$

$CD + 1 = \sqrt{16 - (x-1)^2}$

$(CD + 1)^2 = 16 - (x-1)^2$

$(x-1)^2 = 16 - (CD + 1)^2$

$x-1 = \pm \sqrt{16 - (CD + 1)^2}$

$x = 1 \pm \sqrt{16 - (CD + 1)^2}$