How to Change the Content-Type Meta Tag in Drupal

I'm working on an HTML5 theme for Drupal 7 right now, and I needed to change the meta content-type tag. By default it looks like this: <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />, and I needed the updated HTML5 version: <meta charset="utf-8" />. Normally, you can replace these things in one of the theme template files, but in this case, the meta tag was hard-coded in the Drupal source code somewhere, so I needed a programmatic solution. Here's what I found for both Drupal 6 and 7.

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