so badly/to the extent that

Are these sentences correct?

[color=red]1-He could not cope so badly that he had to be sent back.
[color=blue]2-He did not cope so badly that he had to be sent back.

[color=red]3-He could not cope to the extent that he had to be sent back.
[color=blue]4-He did not cope to the extent that he had to be sent back.

Meaning: His inability to cope was so bad that he had to be sent back.

Gratefully,
Navi.

He could not cope well and had to be sent back.
He coped badly so had to be sent back.