Kuhn-Tucker Conditions and Optimization

I have been trying to solve the following problem.

Maximize z=x-y
subject to: x^2+y^2<=1

The attached file has the work I have done so far. I can't seem to reach plausible solutions.

© BrainMass Inc. brainmass.com March 4, 2021, 5:50 pm ad1c9bdddf
https://brainmass.com/math/optimization/kuhn-tucker-conditions-optimization-13751

$2.49