dropdown doesn't obey centering - twitter-bootstrap-3

Question

I am trying to get a series of controls positioned vertically and centered horizontally. The controls are coming out fine, but when I cause the dropdown to drop down, the dropdown text appears left justified on the screen rather than under the centered dropdown control. I've spend a couple of hours on it and I can't get it right. Help would surely be appreciated. Here is what I am using:
<div style="margin-top:50px; text-align: center;">
<div class="dropdown">
<button class="btn btn-primary dropdown-toggle" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Shift / Project2
<span class="caret"></span></button>
<ul class="dropdown-menu" aria-labelledby="dropdownMenu1">
<li><a class="dropdown-item" href="#">HTML</a></li>
<li><a class="dropdown-item" href="#">CSS</a></li>
<li><a class="dropdown-item" href="#">JavaScript</a></li>
</ul>
</div>
<input autocorrect="off" autocapitalize="off" spellcheck="false" type="text" id="xxx" style="margin-top:50px;">
</div>

Answer 1

You could solve this issue using css like i did here:
http://www.bootply.com/zck8H4EVt4
Just add this to your CSS:
.dropdown-menu {
left: 50%;
transform: translate(-50%, 0);
}
// EDIT:
Sorry, i've forgot about the btn-group class...
Just remove the CSS part from the first solution, add .btn-group to your dropdown and use .clearfix after your btn-group like i did here:
<div style="margin-top:50px; text-align: center;">
<div class="dropdown btn-group">
<button class="btn btn-primary dropdown-toggle" id="dropdownMenu1" aria-expanded="false" aria-haspopup="true" type="button" data-toggle="dropdown">Shift / Project2
<span class="caret"></span></button>
<ul class="dropdown-menu" aria-labelledby="dropdownMenu1">
<li><a class="dropdown-item" href="#">HTML</a></li>
<li><a class="dropdown-item" href="#">CSS</a></li>
<li><a class="dropdown-item" href="#">JavaScript</a></li>
</ul>
</div>
<div class="clearfix"></div>
<input id="xxx" style="margin-top:50px;" spellcheck="false" type="text" autocapitalize="off" autocorrect="off">
</div>
Working example: http://www.bootply.com/lryEFqtmdp