Change mysql root password on Centos7

Stop Mysql

  systemctl stop mysqld

Set Mysql environment option

  systemctl set-environment MYSQLD_OPTS="--skip-grant-tables"

Start Mysql

  systemctl start mysqld

Login to Mysql as root

  mysql -u root

Update the root user password

  mysql> UPDATE mysql.user SET authentication_string = PASSWORD('MyPassword')
  -> WHERE User = 'root' AND Host = 'localhost';
  mysql> FLUSH PRIVILEGES;
  mysql> quit

Stop mysql

  systemctl stop mysqld

Unset the mySQL envitroment option so it starts normally next time

  systemctl unset-environment MYSQLD_OPTS

Start mysql

  systemctl start mysqld

Login to mysql again using your new password:

mysql -u root -p

NB : for 5.7.6 and later, you should use
mysql> ALTER USER 'root'@'localhost' IDENTIFIED BY 'MyNewPass';