Now expand the algebraic terms.
[MATH](x_2 - 8)^2 + (y_2 - 12)^2 = \text {WHAT algebraically?}[/MATH]
[MATH](x_2 - 152)^2 + (y_2 - 12)^2 = \text {WHAT algebraically?}[/MATH]
(X^2)^2+(Y^2)^2+208
and
(X^2)^2+(Y^2)^2+23248
First, since X2, which really ought to be [MATH]x_2[/MATH], looks too much like you mean [MATH]x^2[/MATH] (which is what "x^2" means), and takes longer to write, let's just call the coordinates x and y. So the equations are
[MATH](x-8)^2+(y-12)^2=7921[/MATH]
[MATH](x-152)^2+(y-12)^2=7310.25[/MATH]
I'm guessing you meant to type
[MATH](x_2)^2+(y_2)^2+208[/MATH]
but even that is wrong. You evidently changed [MATH](x-8)^2[/MATH] to [MATH]x^2+8^2[/MATH], which is incorrect.
It appears that you have forgotten how to "expand" (multiply out, eliminate parentheses, or whatever it might be called in your region!) We can either use what some call "FOIL", turning [MATH](x-8)^2[/MATH] to [MATH](x-8)(x-8) = x^2 - 8x - 8x + 64 = x^2-16x+64[/MATH]; or use a formula for the square of a binomial: [MATH](a+b)^2 = a^2 + 2ab + b^2[/MATH]. Does any of that sound familiar?
By the way, one reason we need to see your work is to know what you know and what you never learned or forgot, so we can communicate at the right level for you. If I gave you a "complete" solution, but did so assuming you knew what I mentioned in that last paragraph, it probably wouldn't help. So the more you show us, the better we can tune our help to your needs.