the error is in line#1:

9-24 = -15

25-40 = 15

While techically (meaning the way the equation is being treated with completing the square, radicating [correct word??] etc.) the procedure is correct, you start the "proof" under the false premise that

**-15 = +15**
This triggers a cascade of errors with the rest of the calculation, much like a domino-effect:

In Line #2 you get

**1 = 31 **
In Lines #3 and #4 the equation reads as

**-1 = +1**
The important thing - both in mathematics and in life - is to never take anything for granted but always to check the supposed facts yourself, without blindly relying on others.