Align Buttons Side by Side Bootstrap

You can use an out div with a class btn-group. This helps to align the buttons horizontally. Using col-md-6 for each button div can make the buttons missaligned with unwanted space in between.

<div class="btn-group">
<a href="#" class="btn btn-warning">Talent-signup to find jobs</a>
<a href="#" class="btn btn-success">Talent-signup to find jobs</a>
</div>

Try this for Bootstrap 4.Worked for me

<div class="btn-group" role="group" aria-label="Basic example">
  <button type="button" class="btn btn-secondary">Left</button>
  <button type="button" class="btn btn-secondary">Middle</button>
</div>

1) use display: inline-block

#btnSearch,
#btnClear{
    display: inline-block;
    vertical-align: top;
}

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet"/>
<div class="row">
    <div class="col-sm-12 text-center">
        <button id="btnSearch" class="btn btn-primary btn-md center-block" Style="width: 100px;" OnClick="btnSearch_Click" >button</button>
         <button id="btnClear" class="btn btn-danger btn-md center-block" Style="width: 100px;" OnClick="btnClear_Click" >button</button>
     </div>
</div>

or

2) remove class .center-block

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet"/>
<div class="row">
    <div class="col-sm-12 text-center">
        <button class="btn btn-primary btn-md">button</button>
        <button class="btn btn-danger btn-md">button</button>
     </div>
</div>

<div class="container">
<div class="row">

    <div class="col-xs-6">
        <button class="btn btn-warning btn-block">Talent-signup to find jobs</button>
    </div>
    <div class="col-xs-6">
        <button class="btn btn-success btn-block">Employers- signup to hire talent</button>
    </div>

</div>