"What are the coordinates of the point which has a distance of 0.08m away from the origin. the x and y are both equal to each other and are also negative values?"
I've tried using the distance formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ and the closest number I got was like $0.05656$ for both $x$ and $y$ but I'm not entirely sure how to do it without just putting random numbers into the calculator as trial and error, is there a certain method that I can use to do this or is it just complete trial and error?
You were almost there!
The point you are looking for is one of the intersections between the circle $x^2+y^2=0.8^2$ and the line $y=x$.
Substitute and get
$2x^2=0.0064\to x^2= 0.0032\to x=\pm \sqrt{0.0032}\to x\approx\pm 0.0565685$
The point you need is $(-0.0565685,-0.0565685)$