In "Biblical Perspective" Gordon Snider writes:
The perfect obedience of Christ is a standard that no man on his own can equal. When man compares himself with Christ, he sees how totally impossible it is for him to “establish [his] own righteousness.” Christ did not destroy the law, but His perfect obedience made it forever impossible for man to claim his own righteousness as a reason for salvation. But notice the qualification — to every one that believeth. Once a man believes in Christ as Savior, he abandons any attempt to attain righteousness by his own merit. For those without faith, Christ is not the end of the law for righteousness. They, like the Jews of verse 3, continue the vain effort of salvation by works.
Source: Studies in Romans: Adult Teacher's Insights, page 59.