[Python] Why does torch.autograd.backward() fail after in-place tensor update in PyTorch?

I'm trying to manually implement one step of gradient descent using PyTorch to better understand how autograd works.

Here's the function I'm working with:
y = 3x² + 4x + 9

I initialize x with requires_grad=True and run .backward() after computing y. Then I update x in-place using x -= lr * x.grad and try to call .backward() again — but PyTorch throws a RuntimeError about version mismatch due to in-place modification.

import torch

x = torch.tensor([42.0], requires_grad=True)
y = 3 * x ** 2 + 4 * x + 9
y.backward()
with torch.no_grad():
x -= 0.1 * x.grad
y.backward() # Fails here

Error:
RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation...

I understand that in-place ops can cause issues, but:
What exactly is PyTorch tracking here that's being violated?
What's the correct way to re-run gradient descent steps manually using autograd?
Is there a best practice for updating parameters manually without breaking the graph?

Any clarification or example would be appreciated! Thank you so much

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