God's answer to your guilty conscience is the death of his Son. Your answer to a guilty conscience is usually something you do, like confessing harder, praying more, reading your Bible, paying more than your tithe in the offering and so on. These actions are what the writer to the Hebrews calls "dead works," the very things your conscience needs to be cleansed from and the very things that eventually get you wrapped up in the black shadow of your own guilt.
The Fight: A Practical Handbook for Christian Living