optimisim
乐观 

例句：
The candidate's optimisim about his chances of winning encouraged his supporters.
候选人对于获胜机会的乐观态度，鼓励了他的支持者。

rack one's brain
绞尽脑汁，努力思索
 
例句：
Mr. Brown racked his brain trying to remember where he left the wallet.
布朗先生拼命思索，想记起他把钱包放在什么地方了。
 

I can't leave sb. by himself.
我不能把某人单独留下。

对话：
A: Would you like to go to the concert?
B: I'd love to. But I can't leave my son by himself. I've to take care of him at home.
　　　　　　　　 　　　
A：你想去听音乐会吗？
B：我想去，但是我不能把我的儿子单独留下，我得在家照看他。