OK, Finally I was able to resolve this issue :)
I was searching in the wrong direction, I was looking how to open the URL secured by basic authentication using $.Ajax, where I should search for consuming SOAP service from JavaScript using XMLHttpRequest()
the following is the answer to my question:
var symbol = "MSFT";
var xmlhttp = new XMLHttpRequest();
//xmlhttp.open("POST", "http://www.webservicex.net/stockquote.asmx?op=GetQuote", true);
// if you use username and password to secure your URL
xmlhttp.open("POST", "http://www.webservicex.net/stockquote.asmx?op=GetQuote", true, 'username', 'password');
xmlhttp.onreadystatechange = function() {
if (xmlhttp.readyState == 4) {
console.log(xmlhttp.responseText);
}
}
xmlhttp.setRequestHeader("SOAPAction", "http://www.webserviceX.NET/GetQuote");
xmlhttp.setRequestHeader("Content-Type", "text/xml");
var xml = '<?xml version="1.0" encoding="utf-8"?>' +
'<soap:Envelope xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ' +
'xmlns:xsd="http://www.w3.org/2001/XMLSchema" ' +
'xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/">' +
'<soap:Body> ' +
'<GetQuote xmlns="http://www.webserviceX.NET/"> ' +
'<symbol>' + symbol + '</symbol> ' +
'</GetQuote> ' +
'</soap:Body> ' +
'</soap:Envelope>';
xmlhttp.send(xml);