Can Eternal Life Be Earned by Being Good?

I have been reading through the Bible chronologically this year and currently there have been some reoccurring themes I have noticed in my studies. Also, at my church (Tempe Vineyard Church), we are going through a sermon series of the book of Romans written by Paul the apostle and author of much of the New Testament of the Bible.

The main theme that has been highlighted to me is that salvation and eternal life is something only God can give. It cannot be earned. It cannot be gained by doing good things. It cannot be because of the works of any man.

Paul argues:

 "for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins." (Romans 3:23-25)

Also, I read today in Galatians 2:16, which is also written by Paul, that:

"yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law,because by works of the law no one will be justified."

Through my studies I have come to have a more full understanding of the grace of God. Salvation and eternal life are not something I can earn, but it's a gift of God for those who have faith in Jesus Christ as Lord. Although this is just a portion of scripture, the truth portrays that God is love and that He is truly good in all that he does for all mankind. That every person sins and does wrong, but he still chose to offer his Son for all of mankind.