android custom searchView rounded corners

Question

I want to create an Activity with a SearchView that is not in the ActionBar (in fact, I'm using the NoActionBar theme). Now I want this SearchView to have rounded corners (not the EditText inside the actual SearchView, but the SearchView itself),

like this: Mockup

All I can manage is this: actual SearchView.

Can somebody hint me to what I have to change? XML of the Activity:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:orientation="vertical" android:layout_width="match_parent"
android:layout_height="match_parent"
android:clipChildren="false">
<RelativeLayout
    android:layout_width="match_parent"
    android:layout_height="150dp"
    android:background="@color/theBlue">

    <SearchView
        android:id="@+id/search_view"
        android:layout_width="1000dp"
        android:layout_height="wrap_content"
        android:layout_centerHorizontal="true"
        android:layout_marginTop="20dp"
        android:background="@drawable/bg_white_rounded"
        android:clickable="true"/>
</RelativeLayout>

Code of drawable/bg_white_rounded.xml:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android">
<solid android:color="#ffffff"/>
<corners android:radius="10dp"/>
<padding android:left="0dp"
    android:bottom="0dp"
    android:right="0dp"
    android:top="0dp"/>
</shape>

Code of the Activity:

public class MainActivity extends AppCompatActivity {

SearchView searchView;

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);

    // Get search view and modify it to our needs
    searchView = (SearchView) findViewById(R.id.search_view);
    searchView.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            searchView.onActionViewExpanded();
        }
    });
    //int searchPlateId = searchView.getContext().getResources().getIdentifier("android:id/search_plate", null, null);
    //int searchPlateId = searchView.getContext().getResources().getIdentifier("android:id/search_src_text", null, null);
    int searchPlateId = searchView.getContext().getResources().getIdentifier("android:id/search_badge", null, null);
    View searchPlate = searchView.findViewById(searchPlateId);
    //View searchPlate = searchView.findViewById(android.support.v7.appcompat.R.id.search_src_text);
    searchPlate.setBackgroundResource(R.drawable.bg_white_rounded);
}
}

The commented lines are things I've already tried but didn't work. Thanks!

Answer 1

drawable/bg_white_rounded.xml:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android">
<solid android:color="#ffffff"/>
<corners android:radius="20dp"/>
<padding android:left="15dp"
    android:bottom="15dp"
    android:right="15dp"
    android:top="15dp"/>
</shape>

and in .xml

<SearchView
    ...
    android:submitBackground="@drawable/bg_white_rounded"
    android:background="@drawable/bg_white_rounded"

NOTE: in my situation, solution is combined from above answers. Thanks to @rajan.kali and @A.Kazarovets